# What is the GCF of 54 and 72?

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

## Answer: GCF of 54 and 72 is 18

Two methods to find the GCF of 54 and 72 are explained below.

## Explanation:

GCF (Greatest Common Factor) of 54 and 72 is the greatest number that divides the numbers 54 and 72 exactly without any remainder.

- GCF of 54 and 72 by Listing the Common Factors
- GCF of 54 and 72 by Prime Factorization

### Method 1: GCF of 54 and 72 by Listing the Common Factors

Follow the steps given below to find the GCF of 54 and 72 by Listing the Common Factors.

**Step 1:** List the factors of 54 and 72

**Step 2:** Identify the common factors of 54 and 72

**Step 3:** GCF of 54 and 72 is equal to the highest factor among the common factors of 54 and 72

So, GCF of 54 and 72 is 18

### Method 2: GCF of 54 and 72 by Prime Factorization

Let us represent 54 and 72 as a product of its prime factors.

__Prime factorization__ of 72 is 2 × 2 × 2 × 3 × 3

Prime factorization of 54 is 2 × 3 × 3 × 3

The common factors in the prime factorization of 54 and 72 are 2, 3 and 3

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

This means GCF of 54 and 72 is 2 × 3 × 3 = 18

You can find the GCF in any of the above methods but the solution will be the same, that is, GCF of 54 and 72 is 18