# What is the GCF of 64 and 32?

To find the GCF (Greatest Common Factor) of two numbers, we have to determine the largest possible number which divides the two numbers exactly leaving the remainder as 0.

## Answer: GCF of 64 and 32 is 32

We can explain the GCF of 64 and 32 by the following two methods.

## Explanation:

The greatest common factor of 64 and 32 is the greatest number which divides the numbers 64 and 32 exactly. We will use the two methods to find the GCF of 64 and 32.

- GCF of 64 and 32 by Listing the Common Factors
- GCF of 64 and 32 by Prime Factorization

### Method 1: GCF of 64 and 32 by Listing the Common Factors

The list of factors of 64 and 32 is shown below.

We can observe that the common factor of 64 and 32 is 32

So, the greatest common factor of 64 and 32 is 32

GCF of 64 and 32 is 32

### Method 2: GCF of 64 and 32 by Prime Factorization

Let us express the numbers, 64 and 32 as a product of its prime factors.

Prime factorization of 64 is 2 × 2 × 2 × 2 × 2 × 2

Prime factorization of 32 is 2 × 2 × 2 × 2 × 2

The common prime factor is 2 × 2 × 2 × 2 × 2

GCF of 64 and 32 is the product of the prime factors that are common to the prime factorization of 64 and 32

GCF of 64 and 32 is 32

You can find the GCF in any of the above methods but the solution will be the same.