The HCF of 72 and 120 is 24. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 72 and 120. The greatest number that divides 72 and 120 perfectly without leaving a residual is called the HCF of these numbers. The factors of 72 and 120 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120, respectively.
Also read: Highest common factor
What is the HCF of 72 and 120?
The answer to this question is 24. This article shows how to find the HCF of 72 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 72 and 120?
There are three methods to find the HCF of 72 and 120:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 72 and 120 by Prime Factorisation Method
The prime factorisation of 72 and 120 is given by:
Prime factorisation of 72 = (2 × 2 × 2 × 3 × 3)
Prime factorisation of 120 = (2 × 2 × 2 × 3 × 5)
The common prime factors of 72 and 120 are 2, 2, 2 and 3.
Hence, the HCF of 72 and 120 = 2 × 2 × 2 × 3 = 24.
HCF (72, 120) = 24
HCF of 72 and 120 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing a long division repeatedly is the HCF of 72 and 120.
No further division can be done.
Hence, HCF (72, 120) = 24
HCF of 72 and 120 by Listing Common Factors
To calculate the HCF of 72 and 120 by listing out the common factors, list the factors as shown below:
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
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 72 and 120; they are 1, 2, 3, 4, 6, 8, 12, and 24.
Therefore, the highest common factor of 72 and 120 is 24.
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Video Lesson on Properties of HCF and LCM
HCF of 72 and 120 Solved Example
For two numbers, HCF = 24 and LCM = 360. If one number is 120, find the other number.
Solution:
Given: HCF (x, 120) = 24 and LCM (x, 120) = 360
∵ HCF × LCM = 120 × (y)
⇒ x = (HCF × LCM)/120
⇒ x = (24 × 360)/120
⇒ x = 8640/120 = 72
Therefore, the other number is 72.
Frequently Asked Questions on HCF of 72 and 120
What is the HCF of 72 and 120?
How to find the HCF of 72 and 120 by Prime Factorisation?
⇒ Since 2, 2, 2, 3 are common numbers in the prime factorisation of 72 and 120, HCF (72, 120) = 2 × 2 × 2 × 3 = 24
What is the relation between LCM and HCF of 72, 120?
How to find the HCF of 72 and 120 by long division method?
What are the methods to find the HCF of 72 and 120?
By Long Division
By Listing Common Factors
By Prime Factorisation
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