# What is the GCF of 36 and 49?

GCF of two numbers 36 and 49 is the largest possible number which divides both the numbers exactly.

## Answer: GCF of 36 and 49 is 1

Let us find GCF of 36 and 49

## Explanation:

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

We will use the following two methods to find the GCF of 36 and 49.

- GCF of 36 and 49 by Prime factorization Method
- GCF of 36 and 49 by Listing Method

### Method 1: Find GCF of 36 and 49 by Prime Factorization

In this method, we express 36 and 49 as a product of its prime factors.

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

Prime factorization of 49 is 7 × 7

The common factor of 36 and 49 is 1

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

GCF of 36 and 49 is 1

### Method 2: GCF of 36 and 49 by Listing the Common Factors

In this method, we list all the factors of 36 and 49, then identify the common factors.

The highest among the common factors is the GCF of 36 and 49.

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

The factors of 49 are **1**, 7, 49

The only common factor of 36 and 49 is 1.

So, GCF of 36 and 49 is 1

Irrespective of the method, the solution to our question GCF of 36 and 49 is the same.