The HCF of 96 and 72 is 24. The number which can divide 96 and 72 evenly provides the HCF of 96 and 72. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, and the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Methods such as prime factorisation, long division and listing common factors are used to find the HCF. For a clear-cut knowledge of the HCF concepts, refer to the articles given at BYJU’S.
Also read: Highest common factor
What is the HCF of 96 and 72?
The answer to this question is 24. This article contains details on how the HCF of 96 and 72 is found using three methods. The HCF of 96 and 72, which divides 96 and 72 evenly, is 24.
How to Find HCF of 96 and 72?
The three methods to find the HCF of 96 and 72 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 96 and 72 by Prime Factorisation Method
The prime factorisation of 96 and 72 is given by:
96 = 2 × 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3 × 3
Common prime factors = 2, 2, 2, 3
Therefore, HCF (96, 72) = 24
HCF of 96 and 72 by Long Division Method
The numbers (96, 72) should be divided by their prime factors to get the HCF. The divisor we obtain with zero as the remainder is the HCF of 96 and 72.
No further division can be done.
Hence, HCF (96, 72) = 24
HCF of 96 and 72 by Listing Common Factors
The HCF of 96 and 72 using the listing common factors is provided below:
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
There are 8 common factors of 96 and 72 that are 1, 2, 3, 4, 6, 8, 12 and 24.
Therefore, the highest common factor of 96 and 72 is 24.
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Video Lesson on Properties of HCF and LCM
HCF of 96 and 72 Solved Example
Question: Calculate the HCF of 96 and 72 if the LCM is 288.
Solution:
Given
LCM = 288
We know that
HCF × LCM = 96 × 72
HCF = (96 × 72)/288 = 24
Hence, the HCF is 24.
Frequently Asked Questions on HCF of 96 and 72
What is the HCF of 96 and 72?
Find the HCF of 96 and 72 using the long division method.
List the methods used to find HCF of 96 and 72.
If LCM = 288 and HCF = 24 for two numbers, find the other number when one number is 96.
Consider y as the other number
Given LCM = 288 and HCF = 24
HCF × LCM = 96 × y
y = (HCF × LCM)/96
y = (24 × 288)/96
y = 72
Therefore, the other number is 72.
What is the relation between HCF and LCM of 96 and 72?
The relation between HCF and LCM of 96 and 72 is
HCF × LCM = 96 × 72
HCF × LCM = 6912
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