The HCF of 60 and 72 is 12. The integer which divides 60 and 72 evenly indicates the value of HCF. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, and the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Students can learn the prime factorisation, long division and listing common factors methods used in the estimation of HCF.
What is the HCF of 60 and 72?
The answer to this question is 12. You will learn how the HCF of 60 and 72 is determined in a precise way here. The HCF of 60 and 72 is 12, which divides the given two numbers.
Also read: Highest common factor
How to Find HCF of 60 and 72?
The HCF of 60 and 72 can be found using the methods below:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 60 and 72 by Prime Factorisation Method
The prime factorisation of 60 and 72 is given by:
60 = 2 × 2 × 3 × 5
72 = 2 × 2 × 2 × 3 × 3
Common prime factors of 60 and 72 = 2, 2, 3
Hence, HCF (60, 72) = 2 × 2 × 3 = 12
HCF of 60 and 72 by Long Division Method
We can divide (60, 72) by the prime factors so that the HCF of 60 and 72 can be found using the long division method. The divisor we get with zero as the remainder is the HCF of 60 and 72.
No further division can be done.
Hence, HCF (60, 72) = 12
HCF of 60 and 72 by Listing the Factors
The HCF of 60 and 72 can be determined by listing the common factors as given below:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
There are 6 common factors of 60 and 72, and they are 1, 2, 3, 4, 6 and 12.
Therefore, the highest common factor of 60 and 72 is 12.
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Video Lesson on Properties of HCF and LCM
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HCF of 60 and 72 Solved Example
Question: Find the HCF of 60 and 72 if the LCM is 360.
Solution:
Given
LCM = 360
We know that
HCF × LCM = 60 × 72
HCF = (60 × 72)/360
HCF = 4320/360 = 12
Hence, the HCF is 12.
Frequently Asked Questions on HCF of 60 and 72
What is the HCF of 60 and 72?
How to calculate the HCF of 60 and 72 using the long division method?
List the methods to find HCF of 60 and 72.
If LCM = 360 and HCF = 12 for two numbers, find the other number when one number is 60.
Consider y as the other number
Given LCM = 360 and HCF = 12
HCF × LCM = 60 × y
y = (HCF × LCM)/ 60
y = (12 × 360)/60
y = 72
Therefore, the other number is 72.
Show the relation between HCF and LCM of 60 and 72.
The relation between HCF and LCM of 60 and 72 is
HCF × LCM = 60 × 72
HCF × LCM = 4320
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