# What is the Greatest Common Factor (GCF) of 27 and 120?

Are you on the hunt for the GCF of 27 and 120? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!

Want to quickly learn or show students how to find the GCF of two or more numbers? Play this very quick and fun video now!

First off, if you're in a rush, here's the answer to the question **"what is the GCF of 27 and 120?"**:

GCF of 27 and 120 = 3

## What is the Greatest Common Factor?

Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. It's also commonly known as:

- Greatest Common Denominator (GCD)
- Highest Common Factor (HCF)
- Greatest Common Divisor (GCD)

There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.

For smaller numbers you can simply look at the factors or multiples for each number and find the greatest common multiple of them.

For 27 and 120 those factors look like this:

- Factors for 27: 1,
**3**, 9, and 27 - Factors for 120: 1, 2,
**3**, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120

As you can see when you list out the factors of each number, 3 is the greatest number that 27 and 120 divides into.

## Prime Factors

As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.

List out all of the prime factors for each number:

- Prime Factors for 27: 3, 3, and 3
- Prime Factors for 120: 2, 2, 2, 3, and 5

Now that we have the list of prime factors, we need to find any which are common for each number.

In this case, there is only one common prime factor, 3. Since there are no others, the greatest common factor is this prime factor:

GCF = 3

## Find the GCF Using Euclid's Algorithm

The final method for calculating the GCF of 27 and 120 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators.

If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page.

Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. Grab a pencil and paper and give it a try for yourself. (or just use our GCD calculator - we won't tell anyone!)

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