HCF of 84 and 96

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.

HCF of 84 and 96 1

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.

Related Articles

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

Q1

What is the HCF of 84 and 96?

The HCF of 84 and 96 is 12. To calculate the HCF of 84 and 96, we need to factor each number (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) and choose the highest factor that exactly divides both 84 and 96 .i.e 12.
Q2

How to find the HCF of 84 and 96 by prime factorisation?

To find the HCF of 84 and 96, we need to find the prime factorisation of the given numbers .i.e 84 = 2 × 2 × 3 × 7; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ 2, 2, 3 are common factors in the prime factorisation of 84 and 96. Hence, HCF(84, 96) = 2 × 2 × 3 = 12
Q3

What are the methods to find HCF of 84 and 96?

There are three commonly used methods to find the HCF of 84 and 96. They are:
Long Division
Listing Common Factors
Prime Factorisation
Q4

What is the relation between LCM and HCF of 84 and 96?

The following equation can be used to express the relation between (LCM) Least Common Multiple and HCF(Highest Common Factor) of 84 and 96 .i.e HCF × LCM = 84 × 96.
Q5

How to find the HCF of 84 and 96 by long division method?

To find the HCF of 84 and 96 using the long division method, 96 is divided by 84. The corresponding divisor (12) when remainder equals 0 is the HCF.

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*