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.
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
What is the HCF of 96 and 120?
How to find the HCF of 96 and 120 by prime factorisation?
⇒ 2, 2, 2, 3 are common factors in the prime factorisation of 96 and 120. Hence, HCF(96, 120) = 2 × 2 × 2 × 3 = 24
What are the methods to find HCF of 96 and 120?
Long Division
Listing Common Factors
Prime Factorisation
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