In today's video, we're going to look at how you can find the highest common factor, which you might see shortened to HCF. Now, the highest common factor is literally what it says it is. It's the highest, or biggest, factor that a set of numbers have in common. Generally, though, you'll only be asked to find the highest common factor of a pair of numbers. like 20 and 28. 20 has the factors 1, 2, 4, 5, 10 and 20, while 28 has the factors 1, 2, 4, 7, 14 and 28. So to find the highest common factor, we just need to look for the biggest number that occurs in both of these lists, which is 4. So 4 is the highest common factor of 20 and 28. Have a go at doing the same thing for this one.
So here we're being asked to find the highest common factor of 12 and 18. So the first thing we do is list out all the factors of each, which are 1, 2, 3, 4, 6 and 12. for 12, and 1, 2, 3, 6, 9, and 18 for 18. Then we just look for the biggest number that occurs in both lists. So that's going to mean 6 is the highest common factor. And that's all you have to do to find the highest common factor of a pair of numbers. We can also find the highest common factor using prime factors.
The prime factors of 12 are 2, 2, and 3, because these are the prime numbers that multiply to make 12, while the prime factors of 18 are 2, 3, and 3. Once you have the prime factors, to find the highest common factor of the two numbers, you need to select only the prime factors that appear in both prime factor lists. So in this case, that's a 2 and a 3, and we then multiply these together to get 6, which will be our highest common factor. Now if the same number occurs twice in both lists, then we're gonna have to include it twice.
For example, let's change the 18 to a 20, which has the prime factors 2, 2 and 5. This time the prime factors that appear in both lists are these twos and these twos. So we're gonna have to multiply two times two together to get four as our highest common factor. Try using this technique for this one.
So in this question we're being asked to find the highest common factor of 28 and 42. and we're told the prime factors of each. So to find the hcf, we have to look at the prime factors of both of these, and pick out the numbers that are common to both. So these twos, which they both have, and these sevens, which they both have. Then all we do is multiply these two numbers together. So two times seven, which is fourteen.
And that's our highest common factor. For this next question, we're trying to find the HCF of 132 and 420. So this time, the numbers that occur in both lists will be these 2s, these 2s, and these 3s. So we multiply 2 times 2 times 3, which gives us 12 as our highest common factor. Anyways, that's everything for this video, so hope that made sense, and I'll see you next time.