[Music] in today's video we're looking at what prime factors are and also how we can find them using factor trees all we mean by a prime factor is a factor that's also a prime number so if we took the number 12 which has the factors 1 2 3 4 6 and 12 2 and 3 would be considered prime factors because they're both prime numbers and factors of 12. when you get questions about this sort of topic in the exam they'll normally ask you to write a number as a product of its prime factors and what they mean by this is that they want you to find a set of prime factors that multiply together to give that number so if we were asked to write 12 as a product of its prime factors we'd need to come up with a set of numbers that multiply together to make twelve we already know that two and three are prime factors of twelve but we can't just write two times three because two times three is six not twelve instead we'd have to do two times two times three which are still all prime numbers but now do multiply to give us twelve if you want to find the prime factors of more complicated numbers though like you might need to in the exam you'll need to use a method called a factor tree to understand how these things work let's imagine we were asked to write 220 as a product of its prime factors the first step is to write the number whose prime factors you're trying to find so 220 at the very top of the page then we can start to factorize it by splitting it up into a factor for example here we might do 110 and 2. if one of these is a prime number and hence a prime factor like two is then we can circle it and leave it alone for now but if it's not a prime number like 110 then we have to factorize it again into say 11 and 10. 11 is a prime number so we circle that and then split the 10 into 5 and 2 which also both prime numbers so we can circle them both now that we've finished factorizing it we can write out all our prime factors so 2 2 5 and 11. and it's normally best to put them in ascending order like this which just means from smallest to biggest so basically we found that 220 equals 2 times two times five times eleven and as two occurs twice we should rewrite it as two squared times five times eleven now one thing to clarify here is that it doesn't actually matter which way you factorize it you will always end up with the same prime factors for example we could have split the 220 into 10 and 22 then split the 10 into 5 and 2 and split the 22 into 2 and 11. we'd still have ended up with 2 2 5 and 11 as our prime factors so don't worry about which way you factorize it as long as each time you're making a correct factor then you'll end up with the same answer at the end let's try one more where we're asked to express 112 as a product of its prime factors the word express basically just means write or show so we're doing exactly the same thing as we were in the previous questions to start we put 112 at the top and then we just split it into a factor and the easiest pair if it's an even number will generally be two and whatever else you need in this case 56 so we can circle the two and then split the 56 into two and 28 then the 28 can go into 2 and 14 and finally the 14 can go into 2 and 7. so we can express 112 as two times two times two times two times seven and then we can rewrite it as two to the power of four times seven one last thing to mention is that this whole process we've been covering in this video is sometimes called prime factorization which just means to rewrite a number as a product of its prime factors so in this last question we basically did the prime factorization of 112. anyway that's everything for this video so hope you enjoyed it and found it useful in some way and cheers for watching