How does gcd work in python?

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The Highest Common Factor (HCF), also called gcd, can be computed in python using a single function offered by math module and hence can make tasks easier in many situations.

Naive Methods to compute gcd

Way 1: Using Recursion

Python3

def hcfnaive(a, b):

    if(b == 0):

        return abs(a)

    else:

        return hcfnaive(b, a % b)

a = 60

b = 48

print("The gcd of 60 and 48 is : ", end="")

print(hcfnaive(60, 48))

Output

The gcd of 60 and 48 is : 12

Way 2: Using Loops 

Python3

def computeGCD(x, y):

    if x > y:

        small = y

    else:

        small = x

    for i in range(1, small + 1):

        if((x % i == 0) and (y % i == 0)):

            gcd = i

    return gcd

a = 60

b = 48

print ("The gcd of 60 and 48 is : ", end="")

print (computeGCD(60,48))

Output

The gcd of 60 and 48 is : 12

Way 3: Using Euclidean Algorithm 

Python3

def computeGCD(x, y):

   while(y):

       x, y = y, x % y

    return abs(x)

a = 60

b = 48

print ("The gcd of 60 and 48 is : ",end="")

print (computeGCD(60, 48))

Output:

The gcd of 60 and 48 is : 12

• Both numbers are 0, gcd is 0
• If only either number is Not a number, Type Error is raised.

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Given two numbers. The task is to find the GCD of the two numbers.

Using STL :

In Python, the math module contains a number of mathematical operations, which can be performed with ease using the module. math.gcd() function compute the greatest common divisor of 2 numbers mentioned in its arguments.

Syntax: math.gcd(x, y)

Parameter:

x : Non-negative integer whose gcd has to be computed.

y : Non-negative integer whose gcd has to be computed.

Returns: An absolute/positive integer value after calculating the GCD of given parameters x and y.

Exceptions: When Both x and y are 0, function returns 0, If any number is a character, Type error is raised.

Python3

import math

print("The gcd of 60 and 48 is : ", end="")

print(math.gcd(60, 48))

Output

The gcd of 60 and 48 is : 12

Using Recursion :

Python3

def hcf(a, b):

    if(b == 0):

        return a

    else:

        return hcf(b, a % b)

a = 60

b = 48

print("The gcd of 60 and 48 is : ", end="")

print(hcf(60, 48))

Output

The gcd of 60 and 48 is : 12

Using Euclidean Algorithm :

The Euclid’s algorithm (or Euclidean Algorithm) is a method for efficiently finding the greatest common divisor (GCD) of two numbers. The GCD of two integers X and Y is the largest number that divides both of X and Y (without leaving a remainder).

Pseudo Code of the Algorithm-

1. Let  a, b  be the two numbers
2. a mod b = R
3. Let  a = b  and  b = R
4. Repeat Steps 2 and 3 until  a mod b  is greater than 0
5. GCD = b
6.  Finish

Python3

def gcd(a, b):

    if (a == 0):

        return b

    if (b == 0):

        return a

    if (a == b):

        return a

    if (a > b):

        return gcd(a-b, b)

    return gcd(a, b-a)

a = 98

b = 56

if(gcd(a, b)):

    print('GCD of', a, 'and', b, 'is', gcd(a, b))

else:

    print('not found')

Output

GCD of 98 and 56 is 14