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 4 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 twelve while the prime factors of eighteen are two three and three 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 factorists so in this case that's a two and a three 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 going to 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 2 times 7 which is 14 and that's our highest common factor for this next question we are trying to find the hcf of 132 and 420 so this time the numbers that occur in both lists will be these twos these twos and these threes so we multiply two times two times three 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 you