# What is the GCF of 25 and 75?

GCF of two numbers 25 and 75 is the highest possible number which divides both the numbers exactly.

## Answer: GCF of 25 and 75 is 25.

The greatest common factor or the highest common factor of two numbers is the largest possible number which divides both the numbers exactly without any remainder. It is the largest among all the common multiples of the given numbers.

## Explanation:

Common Methods to Find GCF of 25 and 75

- Prime Factorization Method
- Listing the common factors method

### Method 1: How To Find GCF of 25 and 75 by Prime Factorization

In this method,

- we represent 25 and 75 as a product of its prime factors
- GCF is the product of the factors that are common to each of the given numbers.

Prime factorization of 25 is 5 × 5

Prime factorization of 75 is 3 × 5 × 5

Common factor = 5, 5

GCF is the product of the common prime factors = 5 × 5 = 25

GCF is 25

### Method 2: GCF of 25 and 75 by Listing the Common Factors

In this method,

- We list all the factors of 25 and 75
- Then identify the common factors.
- The highest among the common factors is the GCF of 25 and 75.

Here, if we notice 25 itself is the factor of 75.

Factors of 25: 1, 5, 25

Factors of 75: 1, 3, 5, 15, 25, 75.

Common Factors of 25 and 75: 1, 5, 25.

The greatest common factor= 25, which is the highest among the common factors is the GCF of 25 and 75

GCF of 25 and 75 is 25

Irrespective of the procedure to find the GCF, the solution to our question GCF(25,75) is the same.