The HCF of 96 and 108 is 12. The HCF value divides 96 and 108 evenly with the remainder as zero. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 and the factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. The methods to find the HCF value of two given numbers are prime factorisation, long division and listing common factors. The faculty at BYJU’S use easy steps to help students learn the concepts without any doubts.
Also read: Highest common factor
What is the HCF of 96 and 108?
The answer to this question is 12. The methods to find the HCF of 96 and 108 are provided in this article for students’ reference. The HCF of 96 and 108 is 12 which divides the two given numbers equally.
How to Find HCF of 96 and 108?
The three methods to find HCF of 96 and 108 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 96 and 108 by Prime Factorisation Method
The prime factorisation of 96 and 108, is written as:
96 = 2 × 2 × 2 × 2 × 2 × 3
108 = 2 × 2 × 3 × 3 × 3
Common prime factors of 96 and 108 = 2, 2, 3
Therefore, HCF (96, 108) = 2 × 2 × 3 = 12
HCF of 96 and 108 by Long Division Method
The numbers (96, 108) have to be divided by their prime factors to get the HCF of the numbers. The divisor value when the remainder is zero is the HCF of 96 and 108.
No further division can be done.
Hence, HCF (96, 108) = 12
HCF of 96 and 108 by Listing Common Factors
Learn how to list the common factors to find the HCF of 96 and 108, here:
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
There are 6 common factors of 96 and 108, and they are 1, 2, 3, 4, 6 and 12.
Therefore, the highest common factor of 96 and 108 is 12.
Related Articles
- Prime Factorisation Calculator
- Properties of HCF and LCM
- Prime Factorisation and Division Method for HCF and LCM
- Prime Factorisation
- GCD Calculator
Video Lesson on Properties of HCF and LCM
HCF of 96 and 108 Solved Example
Question: Find the LCM if the product of two numbers is 10368 and HCF is 12.
Solution:
Given
Product = 10368
HCF = 12
LCM × HCF = Product
LCM = Product/HCF
LCM = 10368/12 = 864
Hence, the LCM is 864.
Frequently Asked Questions on HCF of 96 and 108
What is the HCF of 96 and 108?
How to find the HCF of 96 and 108 using the long division method?
What methods can be used to determine HCF of 96 and 108?
Determine the HCF of 96 and 108 using prime factorisation.
Using prime factorisation,
96 = 2 × 2 × 2 × 2 × 2 × 3
108 = 2 × 2 × 3 × 3 × 3
HCF (96, 108) = 2 × 2 × 3 = 12
Therefore, the HCF is 12.
Mention the relation between HCF and LCM of 96 and 108.
The relation between HCF and LCM of 96 and 108 is
HCF × LCM = 96 × 108
HCF × LCM = 10368
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