# What is the HCF of 36 and 63?

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

## Answer: HCF of 36 and 63 is 9

HCF of 36 and 63 is the highest number that divides 36 and 63 exactly leaving the remainder 0.

## Explanation:

We can find the HCF by the following methods.

- Prime factorization Method
- Listing the common factors method

### Method 1: Calculate HCF of 36 and 63 by Prime Factorization

Let us represent 36 and 63 as a product of its prime numbers.

Prime factorization of 36 is 2 × 2 × 3 × 3

Prime factorization of 63 is 3 × 3 × 7

The common factor in the prime factorization of 36 and 63 = 3 × 3

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

So, HCF of 36 and 63 is 9

### Method 2: Calculate HCF of 36 and 63 by Listing the Common Factors

The factors of 36 and 63 are shown below.

Factors of 36: 1, 2, 3, 4, 6, 9, 19, 18, 36

Factors of 63: 1, 3, 7, 9, 91, 63

Clearly, the common factors of 36 and 63 are 1, 3 and 9

The highest common factor of 36 and 63 is 9

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