In this lesson, we're going to learn about prime factorization. First, we need to understand what it means to write numbers in their factored forms. So when we write a number in its factored form, that just means that we're showing it as two or more numbers being multiplied together. So we show it as a product of smaller numbers. So let's take a look at the number 18. There's many different ways that we can write the number 18 as a series of numbers being multiplied together. We can write it as one times 18 because that will equal 18. We can write it as two times nine, and we can write it as three times six. Any of these forms are the factored form of 18, showing the number 18 written as two numbers being multiplied together. But it doesn't have to just be two numbers. Take a look at this. If we write two times three, times three and multiply all those numbers together, they'll equal 18 a s well. And if we look carefully at those numbers, they are all prime numbers. This is called prime factorization - when we show the number in its factored form, where all of the numbers are prime numbers. So prime factorization shows the number written as a product of prime numbers. Let's take a look at this example. The number 15 can be written as three times five. Both of those numbers are prime, so it's in its prime factorization form. The number 28 can be written as two times two times seven. If we multiply all of those numbers together, they will equal 28 and they're also all prime. Even the number 100 can be written in its prime factorization form. Two times two times five times five will equal 100, and all of those numbers are prime. So how can we figure out the prime factorization form of a number? We can use what's called a factor tree. Here's how a factor tree works. Let's say if we want to find the prime factorization of the number 36, the first thing that we're going to do is think of any two numbers that will multiply to give us 36. I'm going to start off with three and twelve, but you could start with other numbers as well. You could do four times nine, you could do two times 18, because in the end we would still get the same answer. So it doesn't matter what two numbers you start with, as long as the product of those numbers is equal to the number at the top. Now, if you notice, three is a prime number. So I can't break that number down any further because it's already prime. So I'm going to put a circle around it to remind me that that little branch of the factor tree can't go any further. But if we take a look at the number twelve, we can break that number down into its factors. And we could do different forms. We could do three times four, two times six. As long as they give us a product of twelve. I'm going to use two and six. The two is prime, so that little branch can't go any farther. I'm going to draw a circle so that I know that part is finished, and then I'll look at the number six. Six can be factored into two times three, and both of those numbers are prime, so we can't go any further. We have prime numbers at the end of all of our little tree branches, so we're finished. So now all we have to do is show all the numbers that we circled written as being multiplied together. So we had two twos, and we have two threes. So we can write it in order as two times two, times three, times three. And if we multiply all four of those numbers together, it would equal 36, and all of those numbers are prime. So this represents the prime factorization of the number 36. So we just learned that prime factorization shows the number written as a product of prime numbers being multiplied together, and that we can use a factor tree to help us find the prime factorization of a number.