# What is the HCF of 72, 108 and 180?

HCF (Highest Common Factor) of two or more numbers is the highest possible number which divides the given numbers exactly without any remainder.

## Answer: HCF of 72, 108 and 180 is 36

We will find HCF of 72, 108 and 180 using two methods.

## Explanation:

HCF of 72, 108 and 180 will the greatest number that divides 72, 108 and 180 exactly, that is, leaving the remainder 0

We will explain two methods to find the HCF of 72, 108 and 180

- Prime Factorization to find HCF of 72, 108 and 180
- Listing the Common Factors to find HCF of 72, 108 and 180

### Method 1: HCF of 72, 108 and 180 by Prime Factorization

Represent 72, 108 and 72 as a product of its prime factors.

Prime factorization of 72 is 2 × 2 × 2 × 3 × 3

Prime factorization of 108 is 2 × 2 × 3 × 3 × 3

Prime factorization of 180 is 2 × 2 × 3 × 3 × 5

The common factor in the prime factorization of 72, 108 and 180 is 2 × 2 × 3 × 3

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

Since the common factor is 36, the HCF of 72, 108 and 72 is 36

### Method 2: HCF of 72, 108 and 180 by Listing the Common Factors

The factors of 72, 108 and 180 are shown below:

The common factors of 72, 108 and 180 are 1, 2, 3, 4, 6, 9, 12, 18 and 36

So, HCF of 72, 108 and 180 is 36

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