Video: AQA GCSE Mathematics Higher Tier Pack 1 β€’ Paper 2 β€’ Question 11

AQA GCSE Mathematics Higher Tier Pack 1 β€’ Paper 2 β€’ Question 11

02:04

Video Transcript

Circle the highest common factor HCF of 10π‘₯ cubed 𝑧 and 15π‘₯ squared 𝑧 cubed. Five π‘₯ squared 𝑧, 150π‘₯ to the fifth 𝑧 to the fourth, 30π‘₯ to sixth 𝑧 to the third, or five π‘₯𝑧.

So when finding the highest common factor, when looking at the numbers themselves that in the 15, we need to break them down into their prime factors.

And to be prime means that it has exactly two factors: itself and one. So 10 could be written as two times five, where two is prime and five is prime. So that’s completely broken down. And for 15, we could rewrite that as three times five. Three is prime and five is prime.

Now, for the variables, it’s not called prime factorization. We just break it down into its single factors and see how many they have in common. So π‘₯ cubed is the same as π‘₯ times π‘₯ times π‘₯, three π‘₯s. And then, 𝑧 is just simply 𝑧 or 𝑧 to the first power.

Now, for π‘₯ squared, for our next expression, it can be written as π‘₯ times π‘₯. And then, 𝑧 cubed can be rewritten as 𝑧 times 𝑧 times 𝑧. So now that both numbers are completely broken down, we want to circle the highest common factor.

And we have four to choose from. So let’s look at these.

For numbers, they both have five. They both have π‘₯s. And the greatest number of π‘₯s that they both have would be two. So we would write that as π‘₯ squared. And the highest number of 𝑧s that they both have would just be 𝑧.

Therefore, the highest common factor between them would be five π‘₯ squared 𝑧. So this will be our final answer.

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