Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 2 • Question 9

GCSE Mathematics Foundation Tier Pack 5 • Paper 2 • Question 9

02:33

Video Transcript

Find the highest common factor, (HCF) of 21, 56, and 112.

To do this, we can create factor trees. So we will be breaking down these numbers into their prime factors. To be prime means to have exactly two factors. For example, two is prime. Two has factors of two and one because two times one is two. Now, one is not prime because one’s factors are one and one for one times one. And there’re not exactly two factors; there’s only exactly one factor. So one is not prime.

So let’s begin by breaking these numbers down. 21 is seven times three. Now, seven is prime because it only has two factors: one and seven and three is prime. So we broke down 21 into its prime factors.

Now, for 56, 56 is eight times seven. Now, eight is not prime; it has more than two factors. So let’s break down eight. Eight is four times two. Four is not prime; four has factors of two and two. And two is prime because two only has two factors: itself and one. So all of the twos are prime and the seven is prime. So we’ve broken this down into its prime factors.

Now for 112, 112 is equal to two times 56. And we know exactly how 56 breaks down because we just did that on the left. 56 is eight times seven. And eight breaks down into four times two and then four breaks down into two times two. So all of these twos are prime and the seven is prime. So we know that 21 is seven times three. 56 is two times two times two which is two cubed times seven. 112 would be two to the fourth power times seven.

So what would be the highest common factor between these three? It would be seven. Two to the third power and two to the fourth power yes indeed are larger. However, 21 does not have a two to any power. So we can’t use that. If it did, we would use the highest power of two that all three of them would have.

But once again, the highest common factor of 21, 56, and 112 would be seven.

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