# What is the GCF of 60 and 84?

Greatest Common Factor is a greatest number that is a factor of two or more other numbers.

The GCF (greatest common factor) is the same as: HCF (Highest Common Factor), GCD (Greatest Common Divisor), HCD (Highest Common Divisor), GCM (Greatest Common Measure), HCM (Highest Common Measure)

## Answer: GCF of 60 and 84 is 12

Two methods to find the GCF of 60 and 84 are explained below.

## Methods to find GCF of 60 and 84

- Prime Factorization
- Long Division

### Method 1: GCF of 60 and 84 by Prime Factorization

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

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

Prime factorization of 84 is 2 × 2 × 3 × 7

The occurrences of common prime factors of 60 and 84 are 2, 2 and 3

Hence GCF(60, 84) is 2 × 2 × 3 = 12

### Method 2: GCF of 60 and 84 by Long Division

- Step 1: Divide the larger number by the smaller
- Step 2: Divide the dividend by the remainder obtained in step 1 and repeat this step until we get the remainder as 0
- Step 3: The last dividend is the GCF of the two numbers

We take the larger value 84 as dividend and smaller value 60 as divisor

We will get the GCF same for the given numbers by using different methods.