# What is the HCF of 6, 72, and 120?

The largest possible number which divides the given numbers exactly without any remainder is called the highest common factor or greatest common factor. Some times it is also termed as GCD (greatest common divisor)

## Answer: HCF of 6, 72, and 120 is 6.

Let's find the HCF of 6, 72, and 120

## Explanation:

The highest common factor can be calculated by the below-mentioned methods

- Listing the common factors method
- Prime factorization method

### Method 1: HCF(6, 72, 120) by Prime Factorization

Here we express the given numbers as the product of their corresponding prime factors.

So, 6 = 2 × 3

72 = 2 × 2 × 2 × 3 × 3

120= 2 × 2 × 2 × 3 × 5

HCF is the product of all such common prime factors.

Therefore HCF(6, 72, 120) is 2 × 3 = 6

### Method 2: HCF of 6, 72, and 120 by Listing the Common Factors

List out all the factors of 6, 72, and 120. Then identify the largest among all the common factors of all the given numbers.

Factors of 6 are 1, 2, 3, and 6.

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

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

Common factors of 6, 72, and 120 are 1, 2, 3, and 6

The highest among them is 6.

So, HCF(6,72,120) is 6.

Thus, HCF of 6, 72, and 120 is 6.