# What is the GCF of 75 and 125?

The largest possible number which exactly divides both the numbers is the GCF of two numbers 75 and 125.

## Answer: GCF of 75 and 125 is 25

Let us find GCF of 75 and 125

## Explanation:

The Greatest common factor of two numbers is the largest possible number which divides both the numbers completely without remainder.

We will use the following two methods to find the GCF of 75 and 125

- GCF of 75 and 125 by prime factorization
- GCF of 75 and 125 by Listing Method

### Method 1: GCF of 75 and 125 by prime factorization

In this method, we represent 75 and 125 as a product of its prime factors.

Prime factorization of 75 is 3 × 5 × 5

Prime factorization of 125 is 5 × 5 × 5

The common factor in the Prime factorization of 75 and 125 is 5 × 5

GCF is the product of the common factors of the given numbers.

GCF of 75 and 125 is 25

### Method 2: GCF of 75 and 125 by Listing the Common Factors

In this method, we list all the factors of 75 and 125, then identify the common factors.

The highest among the common factors is the GCF of 75 and 125.

- Factors of 75 are
**1**, 3,**5**, 15, 25, 75 - Factors of 125 are
**1**, 5, 25, 125

Common Factors of 75 and 125 are 1, 5 and 25

Clearly, the Greatest common factor of 75 and 125 is 25