The highest common factor (often abbreviated to HCF) of 48, 84 and 132 is 12. There are a number of ways to work this out, and everyone seems to be taught different ways of calculating the highest common factor of a series of numbers. Here is one easy way of working out the highest common factor, called a "factor tree". I will use an example with the easy numbers of 24 and 40 so you can follow what is going on.
• At the top of your "factor tree", write the number you are going to start with, e.g. 24
• Draw two "branches" pointing downwards from the top number, 24. At the end one branch, write the smallest number you can divide 24 into (excluding one). In this case, it will be two
• On the other branch pointing downwards from the 24, write the number you get when you divide your top number by the smallest number. In this case, 24 divided by two equals 12, so you write 12 on your other branch
• Two will not divide any further (excluding the use of number one) so leave it. From the 12, use the same steps you used for the 24 - here, 12 can divide by two, leaving you with six, so your two branches from 12 lead to the numbers two and six
• Continue in this way until the number at the end of each branch is as small as it can be (without using number one)
You should do the same for the number 40. Once you have worked out the factors for each number, you should be left with the following:
24 = 3 x 2 x 2 x 2
40 = 5 x 2 x 2 x 2
As you can see from the numbers I have underlined, both 24 and 40 each contain three lots of two. Therefore, you work out 2 x 2 x 2. This leaves you with eight, meaning eight is the highest common factor of 24 and 40. This method can be applied to any size and amount of numbers at one time. Although it appears complex at first, it is very easy, and with practice you will be able to work out the highest common factor of two or more numbers very quickly.
• At the top of your "factor tree", write the number you are going to start with, e.g. 24
• Draw two "branches" pointing downwards from the top number, 24. At the end one branch, write the smallest number you can divide 24 into (excluding one). In this case, it will be two
• On the other branch pointing downwards from the 24, write the number you get when you divide your top number by the smallest number. In this case, 24 divided by two equals 12, so you write 12 on your other branch
• Two will not divide any further (excluding the use of number one) so leave it. From the 12, use the same steps you used for the 24 - here, 12 can divide by two, leaving you with six, so your two branches from 12 lead to the numbers two and six
• Continue in this way until the number at the end of each branch is as small as it can be (without using number one)
You should do the same for the number 40. Once you have worked out the factors for each number, you should be left with the following:
24 = 3 x 2 x 2 x 2
40 = 5 x 2 x 2 x 2
As you can see from the numbers I have underlined, both 24 and 40 each contain three lots of two. Therefore, you work out 2 x 2 x 2. This leaves you with eight, meaning eight is the highest common factor of 24 and 40. This method can be applied to any size and amount of numbers at one time. Although it appears complex at first, it is very easy, and with practice you will be able to work out the highest common factor of two or more numbers very quickly.
