# What is the GCF of 75 and 100?

The greatest common divisor or the greatest common divisor of two or more numbers is the largest possible number which exactly divides the given numbers.

## Answer: The GCF of 75 and 100 is 25

## Explanation:

Methods to find the GCF of 75 and 100 are explained below.

## Methods to find GCF of 75 and 100

GCF or HCF can be calculated in these most common ways:

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

## Find GCF of 75 and 100 by Prime Factorization

Let us represent 75 and 100 as a product of its prime numbers

The Prime factorization of 75 is 3 × 5 × 5 whereas the prime factorization of 100 is 2 × 2 × 5 × 5

Common factors = 5 \(\times\) 5

The greatest common factor(GCF) or the highest common factor is defined as the product of the factors that are common to each of the given numbers.

GCF is 25

### Find GCF of 75 and 100 by Long Division

- Divide 100 by 75 and check the remainder, if it is non-zero proceed to step-2, otherwise move to step-3.
- Make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform the long division again.
- Continue till you get the remainder as 0
- The final divisor is the GCF of the given numbers.

The GCF of 75 and 100 remains same irrespective of the method we choose to find the GCF.