# What is the HCF of 65 and 117?

The largest possible number which divides the given numbers exactly without any remainder is called the highest common factor of the given numbers.

## Answer: HCF of 65 and 117 is 13

Let us see how to find the HCF of 65 and 117

## Methods to Find HCF of 65 and 117

Let us calculate HCF by these most common methods:

- Prime factorization Method
- Long division Method

### Method 1: Calculate HCF of 65 and 117 by Prime Factorization

Let us represent 65 and 117 as a product of its prime numbers

Prime factorization of 65 is 5 × 13

Prime factorization of 117 is 3 × 3 × 13

The product of the prime factors that are common to each of the given numbers is called HCF or GCF.

### Method 2: Calculate HCF of 65 and 117 by Long Division

- Step 1: Divide 117 by 65 and check if the remainder is non-zero, then proceed to step-2 otherwise step-4.
- Step 2: Consider the remainder of the above step as the divisor and the divisor of the above step as the dividend.
- Step 3: Continue the long division till you get the remainder as 0
- Step-4: The divisor when the remainder is 0 is the HCF.

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