# What is the HCF of 84 and 96?

The largest possible number which divides the given numbers exactly without leaving any remainder is called the HCF (Highest Common Factor).

## Answer: HCF of 84 and 96 is 12

HCF of 84 and 96 is the highest number that divides 84 and 96 exactly leaving the remainder 0.

## Explanation:

Look at the methods to find the HCF (84, 96)

- HCF of 84 and 96 by Prime Factorization
- HCF of 84 and 96 by Listing the Common Factors

### Method 1: Find HCF of 84 and 96 by Prime Factorization

Represent 8 and 14 as a product of its prime factors.

Prime factorization of 84 is 2 × 2 × 3 × 7

Prime factorization of 96 is 2 × 2 × 2 × 2 × 2 × 3

The common factor in the prime factorization of 84 and 96 are 2, 2, and 3.

HCF is the product of the factors that are common to each of the given numbers.

So, HCF of 84 and 96 is 2 × 2 × 3 = 12

### Method 2: Find HCF of 84 and 96 by Listing the Common Factors

The factors of 84 and 96 are shown below

There are 6 common factors of 84 and 96, that are, 1, 2, 3, 4, 6 and 12.

The highest common factor of 84 and 96 is 12.

You can find the HCF in any of the above methods but the solution will be the same.