# What is the GCF of 20 and 100?

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 20 and 100 is 20

GCF of 20 and 100 is the highest number that divides 20 and 100 exactly leaving the remainder 0.

## Explanation:

We can find the GCF of 20 and 100 by the following two methods.

- Listing the common factors method
- Prime factorization Method

### Method 1: GCF of 20 and 100 by Listing the Common Factors

Factors of 20: 1, 2, 4, 5, 10, __20__

Factors of 100: 1, 2, 4, 5, 10, ** 20**, 25, 50, 100

Common factors of 20 and 100 are 1, 2, 4, 5, 10 and 20.

We observe that the greatest common factor of 20 and 100 from the list is 20.

So, GCF of 20 and 100 is 20.

### Method 2: GCF of 20 and 100 by Prime Factorization

Let us represent 20 and 100 as a product of their prime factors:

Prime factorization of 20 is 2 × 2 × 5

Prime factorization of 100 is 2 × 2 × 5 × 5

The common factors in the prime factorization of 20 and 100 are 2, 2 and 5.

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

GCF of 20 and 100 is 2 × 2 × 5 = 20

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