The HCF of two numbers is 6 their LCM is 120 if one number is 24 find the other number

Click here to see ALL problems on Mixture Word Problems Question 1120355: the HCF of two numbers is 6 and their lowest common multiple is 120.if one of the numbers is 30.find the other number Answer by greenestamps(11230)     (Show Source): You can put this solution on YOUR website! Nội dung chính Show What is HCF of 96 and 120? Methods to Find HCF of 96 and 120 HCF of 96 and 120 by Long Division HCF of 96 and 120 by Listing Common Factors HCF of 96 and 120 by Prime Factorization HCF of 96 and 120 Examples FAQs on HCF of 96 and 120 What is the HCF of 96 and 120? How to Find the HCF of 96 and 120 by Long Division Method? If the HCF of 120 and 96 is 24, Find its LCM. What is the Relation Between LCM and HCF of 96, 120? What are the Methods to Find HCF of 96 and 120? How to Find the HCF of 96 and 120 by Prime Factorization? For any two numbers, the product of the HCF and LCM of the two numbers is equal to the product of the two numbers. So in this problem if the other number is x then 6*120 = 30*x 720 = 30x x = 720/30 = 24 The other number is 24.

HCF of 96 and 120 is the largest possible number that divides 96 and 120 exactly without any remainder. The factors of 96 and 120 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the HCF of 96 and 120 - prime factorization, long division, and Euclidean algorithm.

What is HCF of 96 and 120?

Answer: HCF of 96 and 120 is 24.

Explanation:

The HCF of two non-zero integers, x(96) and y(120), is the highest positive integer m(24) that divides both x(96) and y(120) without any remainder.

Methods to Find HCF of 96 and 120

Let's look at the different methods for finding the HCF of 96 and 120.

• Long Division Method
• Listing Common Factors
• Prime Factorization Method

HCF of 96 and 120 by Long Division

HCF of 96 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 120 (larger number) by 96 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (96) by the remainder (24).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the HCF of 96 and 120.

HCF of 96 and 120 by Listing Common Factors

• Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
• Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

There are 8 common factors of 96 and 120, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the highest common factor of 96 and 120 is 24.

HCF of 96 and 120 by Prime Factorization

Prime factorization of 96 and 120 is (2 × 2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 3 × 5) respectively. As visible, 96 and 120 have common prime factors. Hence, the HCF of 96 and 120 is 2 × 2 × 2 × 3 = 24.

☛ Also Check:

• HCF of 28 and 56 = 28
• HCF of 6, 72 and 120 = 6
• HCF of 870 and 225 = 15
• HCF of 6, 8 and 12 = 2
• HCF of 135 and 255 = 15
• HCF of 36 and 42 = 6
• HCF of 72 and 84 = 12

HCF of 96 and 120 Examples

1. Example 1: For two numbers, HCF = 24 and LCM = 480. If one number is 120, find the other number.

   Solution:

   Given: HCF (x, 120) = 24 and LCM (x, 120) = 480
   ∵ HCF × LCM = 120 × (x)
   ⇒ x = (HCF × LCM)/120
   ⇒ x = (24 × 480)/120
   ⇒ x = 96
   Therefore, the other number is 96.

2. Example 2: Find the HCF of 96 and 120, if their LCM is 480.

   Solution:

   ∵ LCM × HCF = 96 × 120
   ⇒ HCF(96, 120) = (96 × 120)/480 = 24
   Therefore, the highest common factor of 96 and 120 is 24.

3. Example 3: Find the highest number that divides 96 and 120 exactly.

   Solution:

   The highest number that divides 96 and 120 exactly is their highest common factor, i.e. HCF of 96 and 120.
   ⇒ Factors of 96 and 120:

   • Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
   • Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

   Therefore, the HCF of 96 and 120 is 24.

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FAQs on HCF of 96 and 120

What is the HCF of 96 and 120?

The HCF of 96 and 120 is 24. To calculate the HCF (Highest Common Factor) of 96 and 120, we need to factor each number (factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the highest factor that exactly divides both 96 and 120, i.e., 24.

How to Find the HCF of 96 and 120 by Long Division Method?

To find the HCF of 96, 120 using long division method, 120 is divided by 96. The corresponding divisor (24) when remainder equals 0 is taken as HCF.

If the HCF of 120 and 96 is 24, Find its LCM.

HCF(120, 96) × LCM(120, 96) = 120 × 96
Since the HCF of 120 and 96 = 24
⇒ 24 × LCM(120, 96) = 11520
Therefore, LCM = 480
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What is the Relation Between LCM and HCF of 96, 120?

The following equation can be used to express the relation between LCM and HCF of 96 and 120, i.e. HCF × LCM = 96 × 120.

What are the Methods to Find HCF of 96 and 120?

There are three commonly used methods to find the HCF of 96 and 120.

• By Long Division
• By Prime Factorization
• By Euclidean Algorithm

How to Find the HCF of 96 and 120 by Prime Factorization?

To find the HCF of 96 and 120, we will find the prime factorization of the given numbers, i.e. 96 = 2 × 2 × 2 × 2 × 2 × 3; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 96 and 120. Hence, HCF(96, 120) = 2 × 2 × 2 × 3 = 24
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