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HCF of 96 and 120

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.

1.	HCF of 96 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

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.

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HCF of 96 and 120 Examples

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.
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.
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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