The HCF of 120 and 144 is 51. The greatest possible number that divides 120 and 144 perfectly without any residual is the HCF of 120 and 144. The factors of 120 and 144 are (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and (1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144), respectively. The three most prevalent methods for determining the HCF of 120 and 144 are listing common factors, prime factorisation, and long division.
Also read: Highest common factor
What is the HCF of 120 and 144?
The answer to this question is 24. This article shows how to find the HCF of 120 and 144 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 120 and 144?
There are three methods to find the HCF of 120 and 144:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 120 and 144 by Prime Factorisation Method
The prime factorisation of 120 and 144 is given by:
Prime factorisation of 120 = (2 × 2 × 2 × 3 × 5)
Prime factorisation of 144 = (2 × 2 × 2 × 2 × 3 × 3)
The common prime factors of 120 and 144 are 2, 2, 2 and 3.
Hence, the HCF of 120 and 144 is 2 × 2 × 2 × 3 = 24.
HCF (120, 144) = 24
HCF of 120 and 144 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is the HCF of 120 and 144.
No further division can be done.
Hence, HCF (120, 144) = 24
HCF of 120 and 144 by Listing Common Factors
To calculate the HCF of 120 and 144 by listing out the common factors, list the factors as shown below:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
There are 8 common factors of 120 and 144, and they are 1, 2, 3, 4, 6, 8, 12, and 24.
Therefore, the highest common factor of 120 and 144 is 24.
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Video Lesson on Properties of HCF and LCM
HCF of 120 and 144 Solved Example
For two numbers, HCF = 24 and LCM = 720. If one number is 120, find the other number.
Solution:
Given: HCF (t, 120) = 24 and LCM (t, 120) = 720
HCF × LCM = 120 × (t)
⇒ t = (HCF × LCM)/120
⇒ t = (24 × 720)/120
⇒ t = 17280/120 = 144
Therefore, the other number is 144.
Frequently Asked Questions on HCF of 120 and 144
What is the HCF of 120 and 144?
How to find the HCF of 120 and 144 by long division method?
What are the methods to find HCF of 120 and 144?
By Long Division
By Listing Common Factors
By Prime Factorisation
If the HCF of 144 and 120 is 24, find its LCM.
Since the HCF of 144 and 120 = 24
⇒ 24 × LCM(144, 120) = 17280
Therefore, LCM = 17280/24 = 720
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