# What is the GCF of 72 and 80?

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

## Answer: GCF of 72 and 80 is 8

GCF of 72 and 80 is the highest number that divides 72 and 80 exactly leaving the remainder 0.

## Explanation:

We can find the GCF of 72 and 80 by the following two methods.

- Prime Factorization Method
- Listing Common Factors Method

### Method 1: GCF of 72 and 80 by Prime Factorization

Let us represent 72 and 80 as a product of its prime factors.

Prime factorization of 72 = 2 × 2 × 2 × 3 × 3

Prime factorization of 80 = 2 × 2 × 2 × 2 × 5

The common factor in the prime factorization of 72 and 80 is repeated 2, that is; 2, 2 and 2.

GCF is the product of the factors that are common to the prime factorization of 72 and 80.

This means GCF of 72 and 80 is 2 × 2 × 2 = 8

### Method 2: GCF of 72 and 80 by Listing the Common Factors

Follow the steps given below to find the GCF of 72 and 80 by Listing the Common Factors.

**Step 1:** List the factors of 72 and 80

**Step 2:** Identify the common factors of 72 and 80

**Step 3:** GCF of 72 and 80 is equal to the highest factor among the common factors of 72 and 80

So, GCF of 72 and 80 is 8.

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