Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 18

GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 18

03:51

Video Transcript

Write 48 as a product of its prime factors.

There are three things we really need to pay attention to when answering this question. The first is the word “product.” When we find the product of two numbers, we multiply them. Let’s bear this in mind at the end. The second is this word “prime.” A prime number is a number which has exactly two factors: one and itself.

The first five prime numbers are two, three, five, seven, and 11. It’s important we remember that one is not a prime number. One actually only has one factor since it can be divided by one and itself, itself being one.

And we have to start showing the word “factor.” But let’s remind ourselves what that means. It’s a number that divides evenly into another number, without leaving a remainder. Now, when we write 48 as a product of its prime factors, we tend to use something called a factor tree.

To find the first two numbers in our factor tree, we need to find two numbers that multiplied together to make 48. Ideally, one of these will be prime, but this isn’t entirely necessary. 48 is an even number. That means it can be divided by two. When we divide 48 by two, we get 24. We said that two was a prime number. So we’re going to stop here. We can draw a circle around the number two to show that we’ve finished on this branch.

24 is not a prime number. So we need to find two numbers that again multiplied to make 24. Since 24 is even though, we know it can be divided by two. And when we divide 24 by two, we get 12. Since this two is also a prime number, we put a circle around this. And we finished on this branch.

12 isn’t. So let’s find two numbers that multiply to make 12. 12 is even. So two is a nice, easy number to choose. When we divide 12 by two, we get six. And once again, we pop a circle round the number two because it’s prime. And we’re done with this branch.

Let’s repeat this process for the number six. Six can be divided by two. And when we divide six by two, we end up with three. Both two and three are prime numbers. So we draw circles around them both and we’re done. Remember we said that product means multiply. So the final step is to multiply these numbers together.

48 is equal to two multiplied by two multiplied by two multiplied by two multiplied by three. A common mistake here is to either separate these numbers with commas or to add them altogether. If we do that, we’re going to be losing the final mark in this question. We must make sure we write them as a product.

We also don’t need to evaluate; that’s to find out the answer to two times two times two times two times three because actually it just gives us 48. And another way to write this will be two to the power of four multiplied by three. In fact, in this question, that’s not entirely necessary. But if it had asked us to put it in index form, that’s what this would have look like.

Now, remember we said that we didn’t need to find factors of 48 that were prime numbers straightaway. Let’s see what that would have looked like. Six multiplied by eight is 48. Neither of these are prime numbers. So I’m not going to circle them. Six can be written as two multiplied by three. Since both of these are prime numbers, we can pop a circle around them.

Eight can be written as two multiplied by four. And we’ll pop a circle around that too. And four can be written as two multiplied by two. Once again, we’ve shown that 48 can be written as two multiplied by two multiplied by two multiplied by two and multiplied by three.

In fact, there are a number of different ways that we can write the factor tree for 48. We will always end up with the same answer.

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