The Greatest Common Factor of a set of numbers is often used to help calculate fractions, which are frequently used in everyday life. You can simplify a fraction by finding the highest common factor between the numerator and denominator, which can make it easier to work out more complex calculations.

Learning how to calculate the Greatest Common Factor from a set of numbers is a worthwhile skill to have as it can be applied to various branches of mathematics. There are various methods to calculate it, which can also show you the Lowest Common Factor.

## What does the Greatest Common Factor mean in maths?

The Greatest Common Factor (GCF), otherwise known as the Highest Common Factor or Greatest Common Divisor, is the largest number that can divide evenly into a set of a minimum of two numbers and leave behind a remainder of zero. For example, the GCF of the numbers 12, 20, and 24 is four. Although the numbers can also be evenly divided by two, four is the larger number and, therefore, the Greatest Common Factor.

The largest number of all the factors is the greatest common factor and can be used to find the common denominators. A common denominator can be divided exactly by the denominators in a group of fractions in the same way that the greatest common factor can be divided evenly in a set of individual numbers.

### What is a factor?

**A factor is an integer that can be divided without a remainder**. Every number that is larger than one has two or more factors, so the GCF is whichever of these numbers has the highest value. The first pair of factors is whatever the number is and one. For example, the first factor pair of 21 is one and 21, whilst the second is three and seven.

When a number is divided by a factor, the subsequent answer is the factor’s pair. These two numbers will create the original number when multiplied together.

### How do I calculate the Greatest Common Factor?

There are three main ways to calculate the GCF of two or more numbers. This includes dividing, listing prime factors and prime factorisation (sometimes spelt prime factorization).

A quick and easy way to find the GCF of a set of numbers is to use the **Greatest Common Factor calculator**. This type of calculator allows users to input two or more numbers and then automatically calculate the GCF. The calculator also explains the method behind the calculation, along with a breakdown of the sums to show how the method was applied. Two of the methods used by the calculator include the Euclidean algorithm and the Binary Greatest Common Divisor algorithm.

In some instances, the only common factor between two or more numbers is the default Greatest Common Factor. You can also work out the Lowest Common Factor (LCF) by listing the factors and finding the smallest factor that the original numbers share. The LCF can be found using the same method that you use to find the GCF.

#### Prime Factorisation

This is a method where you find prime numbers that can multiply together to make the original number. For example, you can divide 12 by two, which leaves six. However, six is not a prime number so this can be further divided by two to result in three. As three is a prime number, the final sum would be two multiplied by two multiplied by three, which results in 12.

Some numbers cannot be divided by anything other than themself and one, which means that they are prime numbers and can only be divided by prime factors.

#### List of factors

A simple method to find the GCF is to write a list of all the common multiples that the numbers in a set have and then select the highest common multiple. For example, the GCF for 12 and 24 is 12, as this is the highest common factor that the numbers divide into without leaving a remainder.

### Why do I need to calculate factors?

**Factors are used in everyday life** and are therefore important to understand. For example, you may need to split into groups as part of an activity, and the organiser will need to divide you into equal-sized groups. Common factors can also be used when calculating money and comparing prices for products. For example, there may be two packs of food that contain different amounts of the product for two different prices. It can be helpful to compare the quantity of the product with the price to see which option is better value.

You can also use factors to work out time, as the 12-hour and 24-hour clocks can be divided into smaller segments. This can help you to work out how frequently you need to take medicine, for example, or how to plan your tasks throughout the day.