Factor trees are useful way of showing numbers that divide into the larger number.
They’re basically a picture with the number at the top and its factors below.
So, if we look at the number 42, a typical factor tree could look like either one of these:
Notice that the second line in both trees are different. These are still factors of 42 but, if you follow it through to the third line, you’ll get to the prime* factors. These are the numbers we are interested in.
Multiplying them together will give you the original number, so 42 = 2 x 3 x 7
The idea is that the prime factors will allow you to calculate:
- the HCF – meaning the Highest Common Factor. Where you have 2 or more numbers, it is the largest number that will divide into both. Really useful for simplifying fractions.
2 / 3 is a bit easier to deal with!
- the LCM – meaning the Lowest Common Multiple. Great for adding and subtracting fractions.
See how to add fractions for more details.
Most GCSE factor tree questions are grade 4 and valued at around 4 marks. Although there are a couple of methods to calculate HCF and LCM.
Watch these and try the quick test
How to work out the HCF – the easy way
How to work out the LCM – the easy way
How to work out the HCF and LCM using factor trees
An alternative method is to use short division. It’s quite useful and can be used with algebraic equations relatively easily 🙂
How to work out the HCF and LCM using short division
LCM Word problem Lars, Rita and Alan
* Prime numbers are numbers that are only divisible by themselves and one. In the factor trees shown 2, 3 and 7 are all prime numbers. Click here for How to work out prime factors of a number for a quick reminder.
Watch on YouTube: