# What is the GCF of 21 and 36?

GCF of two numbers 21 and 36 is the largest possible number which divides both the numbers exactly without any remainder.

## Answer: GCF of 21 and 36 is 3

Let us find GCF of 21 and 36

## Explanation:

The greatest common factor (GCF) of two numbers is the largest possible whole number which divides both the numbers exactly without any remainder. It is also called the highest common factor(HCF).

The following two methods are generally used to find the GCF of 21 and 36.

- GCF of 21 and 36 by Prime factorization Method
- GCF of 21 and 36 by Listing Method

### Method 1: Find GCF of 21 and 36 by Prime Factorization

In this method, we express 21 and 36 as a product of its prime factors.

Prime factorization of 21 is 3 × 7

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

The common factor of 21 and 36 is 3

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

GCF of 21 and 36 is 3

### Method 2: GCF of 21 and 36 by Listing the Common Factors

In this method, we list all the factors of 21 and 36, then identify the common factors.

The highest among the common factors is the GCF of 21 and 36.

The factors of 21 are **1**, **3**, 7, 21

The factors of 36 are **1,** 2, **3,** 4, 6, 9, 12, 18, 36

Common Factors of 21 and 36: 1, 3.

The greatest common factor of 21 and 36 is 3

GCF of 21 and 36 is 3

Irrespective of the method, the GCF of 21 and 36 is the same.