# What is the GCF of 25 and 100?

The greatest common factor of two numbers 25 and 100 is the largest number which exactly divides both the numbers.

## Answer: GCF of 25 and 100 is 25

Let us see how to find the GCF of 25 and 100

## Explanation:

The largest possible number which divides both the numbers exactly without any remainder is called the greatest common factor of two numbers. It is also termed as the highest common factor or greatest common divisor.

Ways to Find GCF of 25 and 100

- Prime factorization
- Listing the common factors

### Method 1: Find GCF(25, 100) by Prime Factorization

Let us express 25 and 100 as a product of its factors.

Prime factorization of 25 is 5 × 5

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

Common factor = 5, 5

GCF is the product of the factors that are common to each of the given numbers, GCF = 5 × 5 = 25

GCF(25,100) is 25

### Method 2: Find GCF(25,100) by Listing the Common Factors

In this method,

**Step 1:** we list all the factors of 25 and 100

**Step 2:** Then identify the common factors.

Factors of 25 are 1, 5, 25.

Factors of 100 are 1, 2, 5, 10, 25, 50, 100.

The highest among the common factors is the GCF of 25 and 100.

Common Factors of 25 and 100: 1, 5, 25.

Greatest common factor= 25

GCF of 25 and 100 is 25

Irrespective of the method, the solution to our question GCF(25, 100) is the same.