# What is the HCF of 120 and 75?

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

## Answer: HCF of 120 and 75 is 15

HCF of 120 and 75 is the highest number that divides 120 and 75 exactly leaving the remainder 0.

## Explanation:

We can find the HCF by the following methods.

- HCF of 120 and 75 by Listing Common Factors
- HCF of 120 and 75 by Long Division

### Method 1: Find HCF of 120 and 75 by Listing Common Factors

Write all the factors of 120 and 75.

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

Factors of 75: 1, 3, 5, __ 15__, 25, 75

The common factors of 120 and 75 are 1, 3, 5, and 15

HCF is the highest factor among all the common factors.

Here the highest common factor among 1, 3, 5, and 15 is 15.

So, HCF of 120 and 75 is 15

### Method 2: Find HCF of 120 and 75 by Long Division

The steps to find the HCF(120, 75) by long division are mentioned below:

**Step 1:** Divide 75 by 120 and check the remainder. We get the remainder as 45.

**Step 2:** Make the remainder of the above step 45 as the divisor and the divisor of the above step 75 as the dividend and perform the long division again.

**Step 3:** Continue till you get the remainder as 0 and the last divisor is the HCF of 120 and 75

The highest common factor of 120 and 75 is 15.

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