In today's video, we're looking at what prime factors are, and also at 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. Now 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 12. We already know that 2 and 3 are prime factors of 12, but we can't just write 2 times 3, because 2 times 3 is 6, not 12. Instead, we'd have to do 2 times 2 times 3, which are still... all prime numbers, but now do multiply to give us 12. 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 factorise it by splitting it up into a factor pair. For example, here we might do 110 and 2. If one of these is a prime number, and hence a prime factor, like 2 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 factorise 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 are also both prime numbers, so we can circle them both. Now that we've finished factorising 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've found that 220 equals 2 times 2 times 5 times 11, and as 2 occurs twice, we should rewrite it as 2 squared times 5 times 11. Now, One thing to clarify here is that it doesn't matter which way you factorise it, you'll 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 factorise it.
As long as each time you're making a correct fact of her, 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 need to split it into a factor pair. And the easiest pair, if it's an even number, will generally be 2 and whatever else you need, in this case 56. So we can circle the 2 and then split the 56 into 2 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 2 times 2 times 2 times 2 times 7, and then we can rewrite it as 2 to the power of 4 times 7. 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.