 This video will show how to prime factor numbers. So with prime factors, we need to know what they are. It's any number that has only one and itself as factors. It only has two factors and they will always be one and itself. So the first prime number would be two, then three, five, seven, eleven, thirteen. They go on from there, but these are the first several. So when I want a prime factor, you've probably seen the factor trees. We'll start with the prime number that you know goes into four. We know that to be two. And then two times what gives me four? Well, two times two is four. And then this one would be prime factor. Everything at the end of my little lines is a prime number, so I know I'm done. All right, let's try 34. Now, this is an even number, so I'm going to just start with two. And then two goes into three once, with one left over. And then two goes into 14 seven times. And 17 happens to be a perfect, or a prime number. 17 happens to be a prime number, so this one's done. All right, they're not always so easy. Let's try this one, 75. Well, it's not even, but it is going to be divisible by five because of this last number being a five. Remember, numbers ending in five or zero can be divisible by five. So we take five, and 15 times five would be 75. And 15 is not a prime number, so I have to do it again. And it ends in five, so I know that it's going to be divisible by that prime number five. And five times three is 15. And three is one of my prime numbers up here. So I know that five times five times three is equal to 75. That's the prime factorization of 75. One more. So 160. Well, it's divisible by two. It's divisible by five. I use to start with the smallest number. I don't know why. I might go faster if I did a bigger number, but I always use the smallest number for some reason. So two goes into 16 eight times, and then I have a zero left over, so it would be 80. Again, I could say that it's divisible by two. And if it's divisible by two, then 40 times two is 80. And 40 again is divisible by two, and that would leave me with 20. And 20 again is divisible by two, and that's going to leave me with two times 10. And then 10 is also divisible by two, and it's 10 times five. Now, everything I have is a prime number, because five is a prime number. So if I wanted to write my prime factors out, I have one, two, three, four, five twos. Times two times two times two times one more two times five. And that would be 160. So even if I had started with the five, I would have still had to end up with all these twos eventually. So it all works out.