HCF of 96 and 120

The HCF of 96 and 120 is 24. The greatest number that can divide 96 and 120 perfectly without leaving a remainder is the HCF of 96 and 120. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Listing common factors, prime factorisation and long division are the three most frequent methods used for calculating the HCF of 96 and 120.

Also read: Highest common factor

What is the HCF of 96 and 120?

The answer to this question is 24. This article shows how to find the HCF of 96 and 120 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 96 and 120?

There are three methods to find the HCF of 96 and 120:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 96 and 120 by Prime Factorisation Method

The prime factorisation of 96 and 120 is given by:

Prime factorisation of 96 = (2 × 2 × 2 × 2 × 2 × 3)

Prime factorisation of 120 = (2 × 2 × 2 × 3 × 5) 

Hence, the HCF of 96 and 120 is 2 × 2 × 2 × 3 = 24.

HCF (96, 120) = 24

HCF of 96 and 120 by Long Division Method

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

HCF of 96 and 120

No further division can be done. 

Hence, HCF (96, 120) = 24

HCF of 96 and 120 by Listing Common Factors

To calculate the HCF of 96 and 120 by listing common factors, list the factors as shown below:

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, and they are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the Highest Common Factor of 96 and 120 is 24.

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Video Lesson on Properties of HCF and LCM

HCF of 96 and 120 Solved Example

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

Solution:

Given: HCF (y, 120) = 24 and LCM (y, 120) = 480

It can be written as HCF × LCM = 120 × (y)

⇒ y = (HCF × LCM)/120

⇒ y = (24 × 480)/120

⇒ y = 96

Therefore, the other number is 96.

Frequently Asked Questions on HCF of 96 and 120

Q1

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.
Q2

How to find the HCF of 96 and 120 by prime factorisation?

To find the HCF of 96 and 120, we need to find the prime factorisation of the given numbers .i.e 96 = 2 × 2 × 2 × 2 × 2 × 3; 120 = 2 × 2 × 2 × 3 × 5.
⇒ 2, 2, 2, 3 are common factors in the prime factorisation of 96 and 120. Hence, HCF(96, 120) = 2 × 2 × 2 × 3 = 24
Q3

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. They are:
Long Division
Listing Common Factors
Prime Factorisation
Q4

What is the relation between LCM and HCF of 96 and 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.
Q5

How to find the HCF of 96 and 120 by long division method?

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

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