programming python

HCF của hai số trong Python sử dụng đệ quy

GCD [Số chung lớn nhất] hoặc HCF [Thước chung cao nhất] của hai số là số lớn nhất chia hết cho cả hai số đó.  

Ví dụ: GCD của 20 và 28 là 4 và GCD của 98 và 56 là 14.  

Một cách tiếp cận cũ và đơn giản là thuật toán Euclide bằng phép trừ

Đó là một quá trình lặp lại phép trừ, mang kết quả về phía trước mỗi lần cho đến khi kết quả bằng với bất kỳ số nào bị trừ. Nếu câu trả lời lớn hơn 1, có một GCD [ngoài 1]. Nếu câu trả lời là 1, không có ước chung [ngoài 1], và do đó cả hai số đều nguyên tố cùng nhau

mã giả cho cách tiếp cận trên

def gcd[a, b].
  nếu a == b.
    trả lại a
  nếu a > b.
    gcd[a – b, b]
  other.
    gcd[a, b – a]

Tại một thời điểm nào đó, một số trở thành thừa số của số kia, vì vậy thay vì liên tục trừ đi cho đến khi cả hai bằng nhau, chúng ta kiểm tra xem nó có phải là thừa số của số kia không.  

Ví dụ: giả sử a=98 & b=56  a>b nên đặt a= a-b và b giữ nguyên. Vì vậy  a=98-56=42  & b= 56. Vì b>a, chúng tôi kiểm tra xem b%a==0. vì câu trả lời là không, chúng tôi tiến hành thêm. Bây giờ b>a  vì vậy  b=b-a và a giữ nguyên. Vậy b= 56-42 = 14 & a= 42. Vì a>b, chúng tôi kiểm tra xem a%b==0. Bây giờ câu trả lời là có. Vì vậy, chúng tôi in nhỏ hơn giữa a và b là H. C. F. tôi. e. 42 là  3 lần của 14  do đó HCF là 14.  

tương tự như vậy  khi a=36  & b=60  ,ở đây b>a  do đó b = 24 & a= 36 nhưng a%b. =0. Bây giờ a>b nên a= 12 & b= 24. và b%a==0. nhỏ hơn giữa a và b là 12  trở thành  HCF của 36 và 60.   

Đề xuất thực hành LCM và GCD Hãy thử

Giải pháp đơn giản

Tiếp cận. Để tìm ƯCLN của hai số, trước tiên chúng ta sẽ tìm số nhỏ nhất của hai số đó, sau đó tìm ước chung cao nhất của số nhỏ nhất đó cũng là ước của số kia

C++




GCD of 98 and 56 is 14
367

GCD of 98 and 56 is 14
368

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
370 
GCD of 98 and 56 is 14
371

GCD of 98 and 56 is 14
372

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
9
GCD of 98 and 56 is 14
0

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
2 
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7____08
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
8
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3673

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7_______13679____13680 
GCD of 98 and 56 is 14
3681
GCD of 98 and 56 is 14
3682 
GCD of 98 and 56 is 14
3683
GCD of 98 and 56 is 14
3684

GCD of 98 and 56 is 14
3685
GCD of 98 and 56 is 14
3686

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
3689

GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
3691

C




GCD of 98 and 56 is 14
3692

GCD of 98 and 56 is 14
3693

GCD of 98 and 56 is 14
3694

 

GCD of 98 and 56 is 14
372

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
6

_______07____13704

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3707

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
2 
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7____08
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
8
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3673

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7____006______007
GCD of 98 and 56 is 14
08
GCD of 98 and 56 is 14
09

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
3689

GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
3691

Java




GCD of 98 and 56 is 14
15

GCD of 98 and 56 is 14
16 
GCD of 98 and 56 is 14
17

 

GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
20

GCD of 98 and 56 is 14
7

_______07____1372

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
36
GCD of 98 and 56 is 14
0

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
2 
GCD of 98 and 56 is 14
40
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
42

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
45
GCD of 98 and 56 is 14
41 
GCD of 98 and 56 is 14
47
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
42

GCD of 98 and 56 is 14
50
GCD of 98 and 56 is 14
8
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
8
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7

_______07____13671

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
72

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
78
GCD of 98 and 56 is 14
79
GCD of 98 and 56 is 14
80
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
83____13680 
GCD of 98 and 56 is 14
85
GCD of 98 and 56 is 14
3682 
GCD of 98 and 56 is 14
87
GCD of 98 and 56 is 14
3684 
GCD of 98 and 56 is 14
89

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
93

Python3




GCD of 98 and 56 is 14
94

 

GCD of 98 and 56 is 14
95

 

 

________ 096 ________ 097

GCD of 98 and 56 is 14
7____099

GCD of 98 and 56 is 14
7____001____002 
GCD of 98 and 56 is 14
03
GCD of 98 and 56 is 14
04

 

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
2 
GCD of 98 and 56 is 14
07

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
10
GCD of 98 and 56 is 14
11 
GCD of 98 and 56 is 14
01
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
41 
GCD of 98 and 56 is 14
16 
GCD of 98 and 56 is 14
17
GCD of 98 and 56 is 14
11 
GCD of 98 and 56 is 14
01
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
23

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
8

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
01____028
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
30

 

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
32

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
01

 

 

GCD of 98 and 56 is 14
36

GCD of 98 and 56 is 14
10
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
78

GCD of 98 and 56 is 14
17
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
80

 

GCD of 98 and 56 is 14
43
GCD of 98 and 56 is 14
44____045
GCD of 98 and 56 is 14
46

 

GCD of 98 and 56 is 14
47

C#




GCD of 98 and 56 is 14
48

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
50

GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
53

GCD of 98 and 56 is 14
6

 

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
372

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
69
GCD of 98 and 56 is 14
0

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
2 
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
74
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
8
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
74
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
74
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
8
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
1

 

_______055____13671

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
98
GCD of 98 and 56 is 14
99
GCD of 98 and 56 is 14
00

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
07____13680 
GCD of 98 and 56 is 14
85
GCD of 98 and 56 is 14
3682 
GCD of 98 and 56 is 14
87
GCD of 98 and 56 is 14
3684 
GCD of 98 and 56 is 14
89

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
93

Javascript




GCD of 98 and 56 is 14
18

GCD of 98 and 56 is 14
19

GCD of 98 and 56 is 14
372

GCD of 98 and 56 is 14
21 
GCD of 98 and 56 is 14
22

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25
GCD of 98 and 56 is 14
0

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
2 
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7____08
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
3

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
8
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
48

GCD of 98 and 56 is 14
49

GCD of 98 and 56 is 14
50
GCD of 98 and 56 is 14
3680
GCD of 98 and 56 is 14
52____13682
GCD of 98 and 56 is 14
54
GCD of 98 and 56 is 14
3684
GCD of 98 and 56 is 14
56

GCD of 98 and 56 is 14
57

GCD of 98 and 56 is 14
58

Đầu ra

GCD of 98 and 56 is 14

Độ phức tạp về thời gian. O[min[a,b]] 
Không gian phụ. Ô[1]

Một giải pháp hiệu quả là sử dụng thuật toán Euclide, đây là thuật toán chính được sử dụng cho mục đích này. Ý tưởng là, GCD của hai số không thay đổi nếu một số nhỏ hơn bị trừ khỏi một số lớn hơn.  

C++




GCD of 98 and 56 is 14
367

GCD of 98 and 56 is 14
368

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
370 
GCD of 98 and 56 is 14
371

GCD of 98 and 56 is 14
64

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
7____05 
GCD of 98 and 56 is 14
76

GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

________ 077 ________ 07 ________ 085

GCD of 98 and 56 is 14
86

GCD of 98 and 56 is 14
7____088

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
86

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36703

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36706

GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
86

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3673

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7_______136717
GCD of 98 and 56 is 14
3680
GCD of 98 and 56 is 14
36719
GCD of 98 and 56 is 14
3682
GCD of 98 and 56 is 14
36721
GCD of 98 and 56 is 14
3684
GCD of 98 and 56 is 14
36723

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
3689

GCD of 98 and 56 is 14
1

C




GCD of 98 and 56 is 14
3692

GCD of 98 and 56 is 14
3694

 

GCD of 98 and 56 is 14
64

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
7____05 
GCD of 98 and 56 is 14
76

GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

________ 077 ________ 07 ________ 085

 

GCD of 98 and 56 is 14
7____088

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

 

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36703

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36706

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3673

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7____006______007
GCD of 98 and 56 is 14
08
GCD of 98 and 56 is 14
09

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
3689

GCD of 98 and 56 is 14
1

Java




GCD of 98 and 56 is 14
15

GCD of 98 and 56 is 14
16 
GCD of 98 and 56 is 14
17

 

GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
36792

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7____064

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36810
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36818
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
36824

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
88

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
36824

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
97

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36703

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36706

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136849

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
36854

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
78
GCD of 98 and 56 is 14
79
GCD of 98 and 56 is 14
80
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
36865 
GCD of 98 and 56 is 14
3680 ________ 085
GCD of 98 and 56 is 14
3682 ________ 087____13684 _______ 089

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

Python3




GCD of 98 and 56 is 14
36875

________ 096 ________ 097

 

GCD of 98 and 56 is 14
7____136879

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36882
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
36886

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
17

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36892
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
36886

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
10

 

_______07____136901

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36882
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
36907

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
10

 

_______07____136912

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36915

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36918
GCD of 98 and 56 is 14
28
GCD of 98 and 56 is 14
36920

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36923
GCD of 98 and 56 is 14
28
GCD of 98 and 56 is 14
36925

 

 

GCD of 98 and 56 is 14
36926

GCD of 98 and 56 is 14
10
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
78

GCD of 98 and 56 is 14
17
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
80

_______05____136934

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
43
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
36938
GCD of 98 and 56 is 14
36939
GCD of 98 and 56 is 14
36940
GCD of 98 and 56 is 14
36941
GCD of 98 and 56 is 14
36942
GCD of 98 and 56 is 14
36943

GCD of 98 and 56 is 14
36944
GCD of 98 and 56 is 14
23

GCD of 98 and 56 is 14
7______043____007
GCD of 98 and 56 is 14
36949
GCD of 98 and 56 is 14
46

 

GCD of 98 and 56 is 14
36951

C#




GCD of 98 and 56 is 14
36952

GCD of 98 and 56 is 14
36953

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
50

 

GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
20

GCD of 98 and 56 is 14
7

_______07____136960

_______07____136962

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
76

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
88

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
97

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37005

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37009

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136849

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
37019

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

_______04____007____13680

GCD of 98 and 56 is 14
36813____085____13682 
GCD of 98 and 56 is 14
87
GCD of 98 and 56 is 14
3684

_______137033____089

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
37038

PHP




GCD of 98 and 56 is 14
37039

GCD of 98 and 56 is 14
37040

GCD of 98 and 56 is 14
37041

 

GCD of 98 and 56 is 14
37042

GCD of 98 and 56 is 14
37043

GCD of 98 and 56 is 14
21 
GCD of 98 and 56 is 14
1____137046
GCD of 98 and 56 is 14
37047
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
6

 

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37057

GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
37048 
GCD of 98 and 56 is 14
37057

GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37046
GCD of 98 and 56 is 14
9

 

GCD of 98 and 56 is 14
7____088

GCD of 98 and 56 is 14
7______05
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37077
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7______05
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37091
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
1____137046
GCD of 98 and 56 is 14
28
GCD of 98 and 56 is 14
37048 
GCD of 98 and 56 is 14
37047
GCD of 98 and 56 is 14
37048 
GCD of 98 and 56 is 14
37102

 

GCD of 98 and 56 is 14
7_______07 
GCD of 98 and 56 is 14
1____137046 
GCD of 98 and 56 is 14
37047
GCD of 98 and 56 is 14
37048____028
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37102

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
37113

GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37115

GCD of 98 and 56 is 14
37048 
GCD of 98 and 56 is 14
37117

 

GCD of 98 and 56 is 14
37118 
GCD of 98 and 56 is 14
37119
GCD of 98 and 56 is 14
37120
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37047
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
37102

 

GCD of 98 and 56 is 14
37125

GCD of 98 and 56 is 14
37126

Javascript




GCD of 98 and 56 is 14
18

 

GCD of 98 and 56 is 14
19

 

GCD of 98 and 56 is 14
64

GCD of 98 and 56 is 14
21 
GCD of 98 and 56 is 14
37131

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
7____05 
GCD of 98 and 56 is 14
76

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

 

GCD of 98 and 56 is 14
7____088

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

 

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36703

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
36706

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

 

_______07____137169

GCD of 98 and 56 is 14
7______137171
GCD of 98 and 56 is 14
3680
GCD of 98 and 56 is 14
85
GCD of 98 and 56 is 14
3682 
GCD of 98 and 56 is 14
87
GCD of 98 and 56 is 14
3684 
GCD of 98 and 56 is 14
89

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
37179

 

GCD of 98 and 56 is 14
58

Đầu ra

GCD of 98 and 56 is 14

Độ phức tạp về thời gian. O[min[a,b]]
Không gian phụ. O[min[a,b]]

Cách tiếp cận [Từ trên xuống Sử dụng Ghi nhớ]

C++




GCD of 98 and 56 is 14
367

GCD of 98 and 56 is 14
37182

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
370 
GCD of 98 and 56 is 14
371

 

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
37188

 

GCD of 98 and 56 is 14
372

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
7____05 
GCD of 98 and 56 is 14
76

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

 

GCD of 98 and 56 is 14
7____088

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
7

_______07____137221

_______07____137223

GCD of 98 and 56 is 14
7____05
GCD of 98 and 56 is 14
37226

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37229

 

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
37236

GCD of 98 and 56 is 14
7

_______07____137239

_______07____136944

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
37243

GCD of 98 and 56 is 14
7

_______07____137246

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37229

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3673

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7____137259____137260
GCD of 98 and 56 is 14
37261
GCD of 98 and 56 is 14
37262

GCD of 98 and 56 is 14
7_______136717
GCD of 98 and 56 is 14
3680
GCD of 98 and 56 is 14
36719
GCD of 98 and 56 is 14
3682
GCD of 98 and 56 is 14
36721
GCD of 98 and 56 is 14
3684
GCD of 98 and 56 is 14
36723

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
3689

GCD of 98 and 56 is 14
1

Java




GCD of 98 and 56 is 14
15

GCD of 98 and 56 is 14
16 
GCD of 98 and 56 is 14
37277

GCD of 98 and 56 is 14
16 
GCD of 98 and 56 is 14
17

 

GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
53

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
37287
GCD of 98 and 56 is 14
37288 
GCD of 98 and 56 is 14
0
GCD of 98 and 56 is 14
37290
GCD of 98 and 56 is 14
37291
GCD of 98 and 56 is 14
37292
GCD of 98 and 56 is 14
37291
GCD of 98 and 56 is 14
37294

GCD of 98 and 56 is 14
55

GCD of 98 and 56 is 14
7____064

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
74

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36810
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36818
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
36824

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
88

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
36824

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
37221

_______07____137223

GCD of 98 and 56 is 14
7____05____0043
GCD of 98 and 56 is 14
30
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37229

 

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
37236

GCD of 98 and 56 is 14
7

_______07____137239

_______07____136944

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
37243

GCD of 98 and 56 is 14
7

_______07____137246

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37229

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136849

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
36854

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
082
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
085
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
087
GCD of 98 and 56 is 14
37291
GCD of 98 and 56 is 14
089

GCD of 98 and 56 is 14
7_______0082
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
094
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
096
GCD of 98 and 56 is 14
37291
GCD of 98 and 56 is 14
098

GCD of 98 and 56 is 14
50
GCD of 98 and 56 is 14
100
GCD of 98 and 56 is 14
30
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
78
GCD of 98 and 56 is 14
79
GCD of 98 and 56 is 14
80
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
36865 
GCD of 98 and 56 is 14
3680 ________ 085
GCD of 98 and 56 is 14
3682 ________ 087____13684 _______ 089

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
125

Python3




GCD of 98 and 56 is 14
126

 

GCD of 98 and 56 is 14
127

GCD of 98 and 56 is 14
128
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
130
GCD of 98 and 56 is 14
28
GCD of 98 and 56 is 14
30 
GCD of 98 and 56 is 14
082 
GCD of 98 and 56 is 14
134
GCD of 98 and 56 is 14
135 
GCD of 98 and 56 is 14
136
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
37291
GCD of 98 and 56 is 14
139
GCD of 98 and 56 is 14
082 
GCD of 98 and 56 is 14
141
GCD of 98 and 56 is 14
135 
GCD of 98 and 56 is 14
136
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
37291
GCD of 98 and 56 is 14
139

 

GCD of 98 and 56 is 14
96 
GCD of 98 and 56 is 14
148

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136879

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36882
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
36886

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
17

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36892
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
36886

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
10

 

_______07____136901

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36882
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
36907

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
10

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5
GCD of 98 and 56 is 14
186
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
28
GCD of 98 and 56 is 14
30
GCD of 98 and 56 is 14
36886

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
193

GCD of 98 and 56 is 14
4

_______07____136912

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36915

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
193
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
36918
GCD of 98 and 56 is 14
28
GCD of 98 and 56 is 14
36920

GCD of 98 and 56 is 14
7____136944
GCD of 98 and 56 is 14
23

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
193____002 
GCD of 98 and 56 is 14
36923
GCD of 98 and 56 is 14
28
GCD of 98 and 56 is 14
36925

GCD of 98 and 56 is 14
4

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
193

 

GCD of 98 and 56 is 14
36926

GCD of 98 and 56 is 14
10
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
78

GCD of 98 and 56 is 14
17
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
80

_______05____136934

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
43
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
36938
GCD of 98 and 56 is 14
36939
GCD of 98 and 56 is 14
36940
GCD of 98 and 56 is 14
36941
GCD of 98 and 56 is 14
36942
GCD of 98 and 56 is 14
36943

GCD of 98 and 56 is 14
36944
GCD of 98 and 56 is 14
23

GCD of 98 and 56 is 14
7______043____007
GCD of 98 and 56 is 14
36949
GCD of 98 and 56 is 14
46

 

GCD of 98 and 56 is 14
244

C#




GCD of 98 and 56 is 14
48

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
50

GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
53

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
254
GCD of 98 and 56 is 14
37288 
GCD of 98 and 56 is 14
0
GCD of 98 and 56 is 14
257

GCD of 98 and 56 is 14
55

GCD of 98 and 56 is 14
7____064

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
74

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
76

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
36824

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
88

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
36824

_______07____137221

_______07____137223

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5
GCD of 98 and 56 is 14
302

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
305

 

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

_______04____0312

GCD of 98 and 56 is 14
7

_______07____137239

_______07____136944

_______04____0319

GCD of 98 and 56 is 14
7

_______07____137246

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
305

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136849

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
37019

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
082
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
342

GCD of 98 and 56 is 14
7____0082____007
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
347

_______050____0349

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
4____0358____13680 
GCD of 98 and 56 is 14
85
GCD of 98 and 56 is 14
3682 
GCD of 98 and 56 is 14
87
GCD of 98 and 56 is 14
3684 
GCD of 98 and 56 is 14
89

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
125

Javascript




GCD of 98 and 56 is 14
369

GCD of 98 and 56 is 14
19

________ 0371 ________ 0372 ________ 137288 ________ 0374

 

GCD of 98 and 56 is 14
375

GCD of 98 and 56 is 14
082 
GCD of 98 and 56 is 14
07____0371 
GCD of 98 and 56 is 14
379

GCD of 98 and 56 is 14
7____0381____137288 
GCD of 98 and 56 is 14
374

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
372

GCD of 98 and 56 is 14
21 
GCD of 98 and 56 is 14
37131

GCD of 98 and 56 is 14
6

 

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
7____05 
GCD of 98 and 56 is 14
76

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
79

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

 

GCD of 98 and 56 is 14
7____088

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
91

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
7

_______07____137221

_______07____137223

GCD of 98 and 56 is 14
7____05
GCD of 98 and 56 is 14
37226

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37229

 

GCD of 98 and 56 is 14
7____097

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36700

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
37236

GCD of 98 and 56 is 14
7

_______07____137239

_______07____136944

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
37243

GCD of 98 and 56 is 14
7

_______07____137246

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37229

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

_______07____137169

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____0082
GCD of 98 and 56 is 14
449

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
082
GCD of 98 and 56 is 14
452

GCD of 98 and 56 is 14
7____0454

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7______137171
GCD of 98 and 56 is 14
3680
GCD of 98 and 56 is 14
85
GCD of 98 and 56 is 14
3682 
GCD of 98 and 56 is 14
87
GCD of 98 and 56 is 14
3684 
GCD of 98 and 56 is 14
89

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
468

 

GCD of 98 and 56 is 14
58

Đầu ra

GCD of 98 and 56 is 14

Độ phức tạp về thời gian. O[min[a,b]]
Không gian phụ. Ô[1]

Thay vì thuật toán Euclide bằng phép trừ, có một cách tiếp cận tốt hơn. Chúng tôi không thực hiện phép trừ ở đây. chúng tôi liên tục chia số lớn hơn cho số nhỏ hơn. Có thể tìm hiểu thêm về giải pháp hiệu quả này bằng cách sử dụng toán tử modulo trong thuật toán Euclide

C++




GCD of 98 and 56 is 14
367

GCD of 98 and 56 is 14
368

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
370 
GCD of 98 and 56 is 14
371

GCD of 98 and 56 is 14
475

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
485

GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
86

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3673

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7_______136717
GCD of 98 and 56 is 14
3680
GCD of 98 and 56 is 14
36719
GCD of 98 and 56 is 14
3682
GCD of 98 and 56 is 14
36721
GCD of 98 and 56 is 14
3684
GCD of 98 and 56 is 14
36723

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
3689

GCD of 98 and 56 is 14
1

C




GCD of 98 and 56 is 14
3692

GCD of 98 and 56 is 14
3694

 

GCD of 98 and 56 is 14
64

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
525

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
3671

GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3673

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

GCD of 98 and 56 is 14
7____006______007
GCD of 98 and 56 is 14
08
GCD of 98 and 56 is 14
09

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
3689

GCD of 98 and 56 is 14
1

Java




GCD of 98 and 56 is 14
15

GCD of 98 and 56 is 14
16 
GCD of 98 and 56 is 14
17

 

GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
36792

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7____064

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
74
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36818
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
74
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
525

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136849

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
36854

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
78
GCD of 98 and 56 is 14
79
GCD of 98 and 56 is 14
80
GCD of 98 and 56 is 14
9

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
36865 
GCD of 98 and 56 is 14
3680 ________ 085
GCD of 98 and 56 is 14
3682 ________ 087____13684 _______ 089

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

Python3




GCD of 98 and 56 is 14
36875

GCD of 98 and 56 is 14
96 
GCD of 98 and 56 is 14
148

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136879

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
36892
GCD of 98 and 56 is 14
02
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
41
GCD of 98 and 56 is 14
36886

GCD of 98 and 56 is 14
3685
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
10

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
620
GCD of 98 and 56 is 14
11
GCD of 98 and 56 is 14
5

 

GCD of 98 and 56 is 14
36926

GCD of 98 and 56 is 14
10
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
78

GCD of 98 and 56 is 14
17
GCD of 98 and 56 is 14
02 
GCD of 98 and 56 is 14
80

_______05____136934

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
43
GCD of 98 and 56 is 14
07
GCD of 98 and 56 is 14
36938
GCD of 98 and 56 is 14
36939
GCD of 98 and 56 is 14
36940
GCD of 98 and 56 is 14
36941
GCD of 98 and 56 is 14
36942
GCD of 98 and 56 is 14
36943

GCD of 98 and 56 is 14
36944
GCD of 98 and 56 is 14
23

GCD of 98 and 56 is 14
7______043____007
GCD of 98 and 56 is 14
36949
GCD of 98 and 56 is 14
46

 

GCD of 98 and 56 is 14
36951

C#




GCD of 98 and 56 is 14
36952

GCD of 98 and 56 is 14
36953

GCD of 98 and 56 is 14
369 
GCD of 98 and 56 is 14
50

 

GCD of 98 and 56 is 14
19 
GCD of 98 and 56 is 14
20

GCD of 98 and 56 is 14
7

_______07____136960

_______07____136962

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
1
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
5

GCD of 98 and 56 is 14
7____0669

GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
5 
GCD of 98 and 56 is 14
82

GCD of 98 and 56 is 14
36813
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
77
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
525

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
7

GCD of 98 and 56 is 14
7____136849

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
18 
GCD of 98 and 56 is 14
25 
GCD of 98 and 56 is 14
71 
GCD of 98 and 56 is 14
37019

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
0 
GCD of 98 and 56 is 14
3677

_______04____007____13680

GCD of 98 and 56 is 14
36813____085____13682 
GCD of 98 and 56 is 14
87
GCD of 98 and 56 is 14
3684

_______137033____089

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
37038

PHP




GCD of 98 and 56 is 14
37039

GCD of 98 and 56 is 14
37040

GCD of 98 and 56 is 14
37041

 

GCD of 98 and 56 is 14
37042

GCD of 98 and 56 is 14
37043

GCD of 98 and 56 is 14
21 
GCD of 98 and 56 is 14
1____137046
GCD of 98 and 56 is 14
37047
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
46

GCD of 98 and 56 is 14
6

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
73

GCD of 98 and 56 is 14
7______05____007
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
726

GCD of 98 and 56 is 14
4
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
9

 

GCD of 98 and 56 is 14
7_______07 
GCD of 98 and 56 is 14
1____137048 
GCD of 98 and 56 is 14
37047
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
11
GCD of 98 and 56 is 14
37048 
GCD of 98 and 56 is 14
37102

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
37113

GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37115

GCD of 98 and 56 is 14
37048 
GCD of 98 and 56 is 14
37117

 

GCD of 98 and 56 is 14
37118 
GCD of 98 and 56 is 14
37119
GCD of 98 and 56 is 14
37120
GCD of 98 and 56 is 14
37046 
GCD of 98 and 56 is 14
37047
GCD of 98 and 56 is 14
37048
GCD of 98 and 56 is 14
37102

 

GCD of 98 and 56 is 14
37125

GCD of 98 and 56 is 14
37126

Javascript




GCD of 98 and 56 is 14
18

 

GCD of 98 and 56 is 14
756

 

GCD of 98 and 56 is 14
64

 

GCD of 98 and 56 is 14
21 
GCD of 98 and 56 is 14
759

GCD of 98 and 56 is 14
55

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
73

_______055____05____0765

GCD of 98 and 56 is 14
7
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
85

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
1

GCD of 98 and 56 is 14
55

GCD of 98 and 56 is 14
55
GCD of 98 and 56 is 14
7 
GCD of 98 and 56 is 14
525

GCD of 98 and 56 is 14
1

 

GCD of 98 and 56 is 14
37113

GCD of 98 and 56 is 14
48

GCD of 98 and 56 is 14
49

 

GCD of 98 and 56 is 14
779

 

GCD of 98 and 56 is 14
780

 

GCD of 98 and 56 is 14
58

Đầu ra

GCD of 98 and 56 is 14

Độ phức tạp về thời gian. O[log[min[a,b]].
Không gian phụ. O[log[min[a,b]]

Độ phức tạp về thời gian của thuật toán trên là O[log[min[a,b]]] nguồn gốc của điều này thu được từ phân tích tình huống xấu nhất. Những gì chúng tôi làm là chúng tôi hỏi 2 số nhỏ nhất thực hiện 1 bước là gì, đó sẽ là [1,1]. Nếu chúng ta muốn tăng số bước lên 2 trong khi vẫn giữ các số càng thấp càng tốt, chúng ta có thể lấy các số là [1,2]. Tương tự, với 3 bước, các số sẽ là [2,3], 4 là [3,5], 5 là [5,8]. Vì vậy, chúng ta có thể nhận thấy một mẫu ở đây, đối với bước thứ n, các số sẽ là [fib[n], fib[n+1]]. Vì vậy, độ phức tạp thời gian trong trường hợp xấu nhất sẽ là O[n] trong đó a>= fib[n] và b>= fib[n+1].  

Bây giờ chuỗi Fibonacci là một chuỗi tăng trưởng theo cấp số nhân trong đó tỷ lệ của số hạng thứ n/[n-1] tiến đến [sqrt[5]+1]/2 còn được gọi là tỷ lệ vàng. Vì vậy, chúng ta có thể thấy rằng độ phức tạp thời gian của thuật toán tăng tuyến tính khi các thuật ngữ tăng theo cấp số nhân do đó độ phức tạp thời gian sẽ là log[min[a,b]]

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