# The GCF Calculator

### How to use a GCF Calculator in math-master.org

The greatest common factor calculator is used to calculate the GCF, HCF, and GCD of a set of two or more numbers. It allows you to see all the work using factorizing within seconds. With this find the greatest common factor calculator, you get a solution for your set of numbers instantly.

## What is the Greatest Common Factor?

The purpose of the online GCF calculator is to find the greatest common factor in a set of numbers. This is the largest positive integer that will divide evenly into all the numbers in the set with zero remainder. For instance, from the set of numbers, 15, 35, and 45, the GCF is 5.

## How to Use the GCF Calculator

The GCF finder by MathMaster works by entering 2 or more whole numbers that are separated by spaces of commas. It will then instantly produce the results of the following from your set of numbers:

• Greatest common factor $GCF$

• Highest common factor $HCF$

• Greatest common denominator $GCD$

• Greatest common divisor $GCD$

## How to Find the Greatest Common Factor

Several ways are readily available for finding GCF from a set of numbers. It depends on the set of numbers and how large they are. The Find the Greatest Common Factor calculator also uses these approaches to find the solution:

1. Factoring: List all the factors of each number, and use the GCF calculator to find the largest common factor.

2. Prime Factorization: List all the prime factors of each number, and utilize the GCF finder to identify the largest common number.

3. Euclid’s Algorithm: This one is used when you have more than two very large numbers. The approach is usually complex and time-consuming when done by hand, but the GCF calculator makes it easy by only entering the numbers.

 Finding GCF Example Factoring Prime Factorization Find the GCF of 27 and 18 Find the GCF $120, 50, 20$ Factors of 27 = 1, 3, 9, 27 Factors of 18 = 1, 2, 3, 6, 9, 18 Common factors = 3 and 9 GCF = 9 Prime factorization $120$ = 2 x 2 x 2 x 3 x 5 Prime factorization $50$ = 2 x 5 x 5 Prime factorization $20$ = 2 x 2 x 5  Common prime factors = 2 and 5 GCF = 2 x 5 = 10

## FAQs

1. What’s the standard rule for a GCF finder?

The greatest common factor for a series of numbers is the greatest factor that divides all the numbers without a remainder.

1. How do you solve GCF problems with the online calculator?

Enter your set of numbers in the Find the Greatest Common Factor Calculator, and it will work out the rest.

1. What is the difference between GCF and HCF?

The greatest common factor $GCF$ and the highest common factor $HCF$ are the same.