# What is the GCF of 48 and 60?

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 48 and 60 is 12

Two methods to find the GCF of 48 and 60 are explained below.

## Explanation:

GCF (Greatest Common Factor) of 48 and 60 is the greatest number that divides the numbers 48 and 60 exactly without any remainder.

- GCF of 48 and 60 by Prime Factorization
- GCF of 48 and 60 by Listing the Common Factors

### Method 1: GCF of 48 and 60 by Prime Factorization

Let us represent 48 and 60 as a product of its prime factors.

__Prime factorization__ of 48 is 2 × 2 × 2 × 2 × 3

Prime factorization of 60 is 2 × 2 × 3 × 5

The common factors in the prime factorization of 48 and 60 are 2, 2 and 3

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

This means GCF of 48 and 60 is 2 × 2 × 3 = 12

### Method 2: GCF of 48 and 60 by Long Division Method

Follow the steps given below to find the GCF of 48 and 60 by Listing the Common Factors.

**Step 1:** Divide 60 by 42 and check the remainder. Here, the remainder is 12

**Step 2:** Make the remainder 12 as the divisor and the divisor 48 as the dividend and perform the long division again.

**Step 3:** Continue till you get the remainder as 0 and the GCF of 48 and 60 is the last divisor of the division process.

So, GCF of 48 and 60 is 12

You can find the GCF in any of the above methods but the solution will be the same, that is, GCF of 48 and 60 is 12