# What is the GCF of 16 and 36?

GCF (Greatest Common Factor) of two numbers is the largest possible number which divides the two numbers exactly without leaving any remainder.

## Answer: GCF of 16 and 36 is 4

We will explain two methods to find the GCF of 16 and 36

## Explanation:

The two methods that we are using to find GCF of 16 and 36 are shown below.

- GCF of 16 and 36 by Long Division
- GCF of 16 and 36 by Prime Factorization

### Method 1: GCF of 36 and 16 by Long Division

The steps to find the GCF(16, 36) by long division are mentioned below.

**Step 1:** Divide 16 by 36 and check the remainder. We get the remainder of 4

**Step 2:** Make the remainder of the above step 4 as the divisor and the divisor of the above step 16 as the dividend and perform the long division again.

**Step 3:** Now we get the remainder as 0, therefore the GCF of 16 and 36 is 4.

Since the remainder is 0 in the second step, therefore the GCF of 36 and 16 is 4.

### Method 2: GCF of 16 and 36 by Prime Factorization

We will represent 16 and 36 as a product of their prime factors.

Prime factorization of 16 is 2 × 2 × 2 × 2

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

Common prime factors are repeated 2, that is; 2 and 2.

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

GCF of 16 and 36 is 2 × 2 = 4

Irrespective of the method, the solution to our question GCF of 16 and 36 is the same.