HCF of 84 and 108

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.

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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Video Lesson on Properties of HCF and LCM

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

Q1

What is the HCF of 84 and 108?

The HCF of 84 and 108 is 12. To calculate the HCF (Highest Common Factor) of 84 and 108, we need to factor each number and choose the highest factor that exactly divides both 84 and 108, i.e., 12.
Q2

How to Find the HCF of 84 and 108 by Prime Factorisation?

To find the HCF of 84 and 108, we will find the prime factorization of the given numbers, i.e. 84 = 2 × 2 × 3 × 7; 108 = 2 × 2 × 3 × 3 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 84 and 108. Hence, HCF(84, 108) = 2 × 2 × 3 = 12
Q3

What are the Methods to Find HCF of 84 and 108?

There are three commonly used methods to find the HCF of 84 and 108.
By Long Division
By Listing Common Factors
By Prime Factorisation
Q4

What is the Relation Between LCM and HCF of 84, 108?

The following equation can be used to express the relation between Least Common Multiple and HCF of 84 and 108, i.e. HCF × LCM = 84 × 108.
Q5

How to Find the HCF of 84 and 108 by Long Division Method?

To find the HCF of 84, 108 using long division method, 108 is divided by 84. The corresponding divisor (12) when remainder equals 0 is taken as HCF.

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