**Maths GCSE Revision - Lesson #5 - Highest Common Factors**

This lesson from the ‘Number’ section of GCSE Maths is all about Highest Common Factors, and using Prime Factors to help find them (transcript below video).

The highest common factor of a pair of numbers, is the biggest number that will divide in to both. The easiest way to find this is to list the factors of both numbers, and look for the biggest factor that they both have in common. Let’s look at this example, where we are asked to find the highest common factor of 12 and 18. We need to write down all of the factors of each number.

The factors of 12 are; 1, 2, 3, 4, 6 and 12.

The factors of 18 are; 1, 2, 3, 6, 9 and 18.

You can see these lists have a few numbers in common. They both include 1, 2, 3 and 6. Out of these, 6 is the largest, which means that the highest common factor of 12 and 18 is 6.

Similar to finding the lowest common multiple (LCM) of two numbers, there is another method you can use to find the highest common factor (HCF) between two numbers. I will show you how to do this method, by going through an example exam question next.

Here is our example exam question, which involves finding highest common factors. It is the same question that we used in the previous section (involving LCMs, and you can see this method in blue). Up to a certain point, it is the same method for finding both the LCM and HCF. Firstly, you write your two numbers as a product of their prime factors, which we already have written at the top. We then have to put these prime factors in to the following Venn diagram, with any common prime factors in the middle section. To find the LCM, we had to multiply together *all *of the numbers in the diagram. To find the HCF, we now want to multiply together all of the numbers that are in the *central section only*. In our middle section, we have two 2s. Which means our highest common factor (HCF) = 2 x 2 = 4, for the numbers 28 and 8. Drawing this diagram is a really great method if you are asked to find both the LCM and the HCF in the same question. Once you have the diagram you can use it to find both answers.

To recap, to find the LCM you multiply together *all of the numbers *in your Venn diagram, and to find the HCF you multiply together *numbers in the central section only.*

Thanks for watching, and if you have any questions about the topics talked about, or you are stuck on a particular concept, just get in touch and we will get back to you as soon as possible!