# What is the GCF of 52 and 65?

GCF of two numbers 52 and 65 is the largest possible number which divides both the numbers exactly.

## Answer: GCF of 52 and 65 is 13

We will see different methods to find the GCF(52,65)

## Explanation:

The greatest common factor of two numbers is the largest possible number which divides both the numbers exactly without any remainder.

We can find the GCF of the numbers in many ways the commonly used methods are listed below.

## Methods to Find GCF of 52 and 65

- Prime factorization
- Listing the common factors me thod

### Method 1: GCF of 52 and 65 by Prime Factorization

In this method, we represent 52 and 65 as a product of its prime numbers

Prime factorization of 52 is 2 × 2 x 13

Prime factorization of 65 is 5 x 13

Common factor = 13

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

GCF is 13

### Method 2: GCF of 52 and 65 by Listing the Common Factors

The list of all the factors of 52 and 65 are written and, then we identify the common factors.

The highest among the common factors is the GCF of 52 and 65.

The factors of 52 are **1,** 2, 4, **13,** 26, 52

The factors of 65 are **1,** 5, **13,** 65

Common Factors of 52 and 65: 1, 13

Greatest common factor= 13

GCF of 52 and 65 is 13

Irrespective of the method, the solution to our question GCF of 52 and 65 is the same.