# What is the HCF of 72 and 120?

HCF of two numbers 72 and 120 is the largest possible number which divides both the numbers exactly.

## Answer: HCF of 72 and 120 is 24

Let us find HCF of 72 and 120.

## Explanation:

The highest common factor (HCF) of two numbers is the largest possible number which divides both the numbers exactly without any remainder.

We will use the following two methods to find the HCF of 72 and 120.

- HCF of 72 and 120 by Prime factorization Method
- HCF of 72 and 120 by Listing Method

### Method 1: HCF of 72 and 120 by Prime Factorization

In this method, we represent 72 and 120 as a product of its prime numbers.

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

Prime factorization of 120 is 2 × 2 × 2 × 3 × 5

Common factors of 72 and 120 are 2, 2, 2, and 3

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

So, HCF of 72 and 120 is 24.

### Method 2: HCF of 72 and 120 by Listing the Common Factors

In this method, we list all the factors of 72 and 120, then identify the common factors.

The highest among the common factors is the HCF of 72 and 120.

Factors of 72 are **1**, **2**, **3**, **4**, **6**, **8**, 9, **12**, 18, **24**, 36, 72

Factors of 120 are **1**, **2**, **3**, **4**, 5, **6**, **8**, 10, **12**, 15, 20, **24**, 30, 40, 60, 120

Common Factors of 72 and 120 are 1, 2, 3, 4, 6, 8, 12, and 24.

The greatest common factor of 72 and 120 is 24