Maths GCSE Revision - Lesson #3
This lesson from the ‘Number’ section of GCSE Maths is all about Prime Numbers, and using them to create ‘Factor Trees’ for certain numbers (transcript below video).
We’re going to look at prime numbers. Prime numbers only have two factors, which are itself and ‘1’. Let’s go through some examples. The number 2 can only be divided by itself and 1, so it is a prime number, as is 3. 4 doesn’t count as a prime number, as that can be divided by 2. If we keep going up, we get 5, 7, 11, 13, 17, and this goes on and on.
Sometimes in the exam, you may be asked to find the prime factors of a number. The easiest way to do this is using a factor tree. Let’s have a look at that in the context of an exam question.
Here’s an example of a typical exam question you might get. We can ignore part ‘a’ for now, as we haven’t gone through that topic area. Part ‘b’ we can go through, and they want us to express 72 as a product of it’s prime factors. We’ve just had a look at what prime numbers are, and the easiest way to do this question is to use something called a ‘prime factor tree’. You start with 72 at the top of your tree, and you split it up in to two numbers that multiply together to give you 72. The simplest thing to do is to split it in half, if possible. That would give us 2 and 36 (as 2 x 36 = 72), and because 2 is a prime number you circle it, and that part of the tree stops there. We can carry on with 36, and if you halve it as before, we get 2 and 18. Again, 2 is a prime number, so we circle that number. 18 can be split up in to factors of 2 and 9 (circle the 2). We are now left with 9, which we cannot be split in half, but we can divide it by 3 (as 3 x 3 = 9). This gives us two 3s, which are prime numbers. This means we can circle both of these, which finishes off our tree, as all of our numbers are circled at the ends of our ‘branches’.
To write 72 as a product of all of these prime numbers, you simply multiply them together (2 x 2 x 2 x 3 x 3 = 72). If you want to go one step further, you can combine these numbers in to indices (2^3 x 3^2 = 72), and that would be your final answer.
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