# What is the HCF of 120 and 144?

The highest common factor(HCF) of two numbers 120 and 144 is the largest possible number which divides both the numbers exactly.

## Answer: HCF of 120 and 144 is 24

Lets see how to find the HCF of 120 and 144

## Explanation:

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

## Methods to Find HCF(120,144)

- Prime factorization
- Listing the common factors

### Method1: HCF of 120 and 144 by Prime Factorization

In the process of prime factorization, we represent 120 and 144 as a product of its prime factors.

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

Prime factorization of 144 is 2 × 2 × 2 × 2 × 3 × 3

Common factor = 2, 2, 2, 3

HCF = product of the factors that are common to each of the given numbers = 2 × 2 × 2 × 3

HCF is 24

### Method 3 : HCF of 120 and 144 by Listing the Common Factors

Here, we initially list all the factors of 120 and 144, then identify the common factors.

HCF of 120 and 144 is the highest among the common factors.

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

The list of factors of 144 are **1,** **2,** **3,** **4,** **6,** **8,** 9, **12,** 16, 18, **24,** 36, 48, 72, 144

Common Factors of 120 and 144: 1, 2, 3, 4, 6, 8, 12, 24.

Greatest common factor = 24

HCF of 120 and 144 is 24

Irrespective of the method, the HCF of 120 and 144 remains the same.