 If you count the number of factors of any perfect square, a number resulting from multiplying an integer by itself, you'll notice that it's always odd. In fact, all square numbers have an odd number of factors, and all non-square numbers have an even number of factors. To understand why, let's look at some examples. 12 isn't a square number, so it should have an even number of factors. We can find 12's factors by routing out all the ways we can multiply two numbers to get 12. The bottom half is just the top half but reversed, so we can ignore those. There are three ways left that we can make 12. There aren't any numbers being used twice in these multiplication statements since that wouldn't make sense. For example, the only number that 3 can multiply with to get 12 is 4. The same goes for all the other numbers. Since each multiplication statement has two numbers, the number of factors will be a multiple of two, and being a multiple of two is the definition of being even. Let's take a look at a perfect square to see what's different about them. Once again, we'll remove the bottom half. Since perfect squares, by definition, are numbers that can be found by multiplying a whole number by itself, perfect squares will always have one multiplication statement in this list with the same number twice, multiplied by itself. All the other ways to get the square will have two different numbers, so that part will be even. Add one to that for the square root and makes it odd. Thanks for watching.