The HCF of 84 and 108 is 12. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 84 and 108. The greatest number that divides 84 and 108 perfectly without leaving a residue is the HCF of 84 and 108. (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and (1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108), respectively, are the factors of 84 and 108.
Also read: Highest common factor
What is the HCF of 84 and 108?
The answer to this question is 12. This article shows the HCF of 84 and 108 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 108?
There are three methods to find the HCF of 84 and 108:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 84 and 108 by Prime Factorisation Method
The prime factorisation of 84 and 108 is given by:
Prime factorisation of 84 = (2 × 2 × 3 × 7)
Prime factorisation of 96 = (2 × 2 × 3 × 3 × 3)
Hence, the HCF of 84 and 108 is 2 × 2 × 3 = 12.
HCF (84, 108) = 12
HCF of 84 and 108 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 84 and 108.
No further division can be done.
Hence, HCF (84, 108) = 12
HCF of 84 and 108 by Listing the Factors
To calculate the HCF of 84 and 108 by listing out the 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 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Therefore, the HCF of 84 and 108 is 12.
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HCF of 84 and 108 Solved Example
Find the highest number that divides 84 and 108 exactly.
Solution:
The highest number that divides 84 and 108 exactly is their highest common factor, i.e. HCF of 84 and 108.
⇒ Factors of 84 and 108:
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Therefore, the HCF of 84 and 108 is 12.
Frequently Asked Questions on HCF of 84 and 108
What is the HCF of 84 and 108?
How to Find the HCF of 84 and 108 by Prime Factorisation?
⇒ Since 2, 2, 3 are common terms in the prime factorization of 84 and 108. Hence, HCF(84, 108) = 2 × 2 × 3 = 12
What are the Methods to Find HCF of 84 and 108?
By Long Division
By Listing Common Factors
By Prime Factorisation
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