Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 12

Which of the following numbers has exactly four factors? Circle your answer. [A] 12 [B] 9 [C] 6 [D] 11

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Video Transcript

Which of the following numbers has exactly four factors? Circle your answer. 12, nine, six, or 11.

First, we remember that numbers that we multiply together to get another number are factors. We’ll need to find the factors of all four of these numbers to find out which one has exactly four. To get 12, we could multiply one times 12. We could also multiply two times six or three times four. So 12 has six factors. One, two, three, 12, six, and four.

What about nine? Well, we can multiply one and nine together to get nine. Or we could multiply three by three. How many factors does nine have? Well, nine only has three unique factors. We wouldn’t count this three a second time.

Next, we’ll think about six. We could multiply one and six together or two and three. This means that six has four unique factors. One, two, six, and three. We’ll go ahead and circle six. But let’s check 11 just to make sure. We recognise that 11 has the factors one and 11. And these are 11’s only factors. It has two factors and is a prime number.

So out of these four values, only the number six has exactly four factors.

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