The HCF of 84 and 96 is 12. The listing common factors, prime factorisation and long division are the three most frequent methods for calculating the HCF of 84 and 96. The greatest possible number that divides 84 and 96 exactly and without a remainder is the HCF of 84 and 96. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, respectively, are the factors of 84 and 96.
Also read: Highest common factor
What is the HCF of 84 and 96?
The answer to this question is 12. This article shows how to find the HCF of 84 and 96 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 84 and 96?
There are three methods to find the HCF of 84 and 96:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 84 and 96 by Prime Factorisation Method
The prime factorisation of 84 and 96 is given by:
Prime factorisation of 84 = (2 × 2 × 3 × 7)
Prime factorisation of 96 = (2 × 2 × 2 × 2 × 2 × 3)
Hence, the HCF of 84 and 96 is 2 × 2 × 3 = 12.
HCF (84, 96) = 12
HCF of 84 and 96 by Long Division Method
The divisor that we get when the remainder is 0 after doing long division repeatedly is the HCF of 84 and 96.
No further division can be done.
Hence, HCF (84, 96) = 12
HCF of 84 and 96 by Listing Common Factors
To calculate the HCF of 84 and 96 by listing common factors, list the factors as shown below:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
There are 6 common factors of 84 and 96, and they are 1, 2, 3, 4, 6, and 12. Therefore, the Highest Common Factor of 84 and 96 is 12.
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Video Lesson on Properties of HCF and LCM
HCF of 84 and 96 Solved Example
The product of two numbers is 8064. If their HCF is 12, what is their LCM?
Solution:
Given: HCF = 12 and product of numbers = 8064
We have LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 8064/12
Therefore, the LCM is 672.
Frequently Asked Questions on HCF of 84 and 96
What is the HCF of 84 and 96?
How to find the HCF of 84 and 96 by prime factorisation?
⇒ 2, 2, 3 are common factors in the prime factorisation of 84 and 96. Hence, HCF(84, 96) = 2 × 2 × 3 = 12
What are the methods to find HCF of 84 and 96?
Long Division
Listing Common Factors
Prime Factorisation
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