# What is the GCF of 48 and 84?

The GCF of two natural numbers x and y is the largest possible number which divides both x and y.

## Answer: GCF of 48 and 84 is 12

Let's find the GCF of 48 and 84

## Explanation:

We can find the GCF by the following methods

- Prime factorization Method
- Listing the common factors Method
- Long division Method

### GCF of 48 and 84 by Prime Factorization

Here 48 and 84 are represented as a product of their prime numbers:

Prime factorization of 48 is 2 x 2 x 2 x 2 x 3

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

Common factors = 2, 2, 3

The product of the factors that are common to each of the given numbers gives us the GCF.

GCF is 2 x 2 x 3 = 12

### GCF of 48 and 84 by Listing the Common Factors

Factors of 48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

Factors of 45 : 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84

Common Factors of 15 and 45 : 1, 2, 3, 4, 6, and 12

Greatest Common Factor from the list = 12

GCF of 48 and 84 is 12