# What is the HCF of 90 and 105?

The Highest Common Factor (HCF) of two numbers is the highest possible number which divides both the numbers exactly. HCF of a and b is denoted by HCF(a, b).

## Answer: HCF of 90 and 105 is 15

HCF of 90 and 105 is the highest number that divides 90 and 105 exactly leaving the remainder 0.

## Explanation:

We will use two methods to find the HCF of 90 and 105.

- HCF of 90 and 105 by Prime Factorization
- HCF of 90 and 105 by Listing the Common Factors

### Method 1: Find HCF of 90 and 105 by Prime Factorization

Prime factorization of 90 is 2 × 3 × 3 × 5

Prime factorization of 105 is 3 × 5 × 7

The common factor in the prime factorization of 90 and 105 are 3 and 5.

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

So, HCF of 906 and 690 is 3 × 5 = 15

### Method 2: Find HCF of 90 and 105 by Listing the Common Factors

The factors of 90 and 105 are shown below.

The common factors of 90 and 105 are 1, 3, 5 and 15.

The highest common factor of 90 and 105 is 15.

The solution of HCF of 90 and 105 will be the same from both the above methods.