Understanding factor pairs

What we're going to do in this video is talk about factors and factor pairs. Now when we talk about factors, these are really numbers that can be multiplied together to make some number. So for example, if I were to talk about factors of 6, I could multiply 2 times 3 to get 6, and so we would say that 2 and 3 are factors of 6.

In fact, we would also say that 2 and 3 is a factor pair for 6 because when I multiply those two, I can get 6. Now to think about all of the different factor pairs for a number, we could think about it in terms of area. How can we make a rectangle with area 6? Well, you could do it if it's 2 units by 3 units, so it could look something like this. I'll just hand draw it.

So let's say a rectangle looks like this. So it has 2 rows and then three columns, and let's say these all have equal area. It's hand drawn, but you can see that the area here would be two times three, which would be equal to six square units. Now, what if what are other ways to get to an area of six? Well, you could have something that is one row, but then it has six columns. So maybe it looks something like this. It looks like this.

So it's one row, and then you have one, two, three, four, five, and I want them all to be roughly the same size. So one times six would be also an area of six. So that would be another factor pair. We know that two times three is equal to six, and we know that one times six is equal to six, and these are actually the two factor pairs for six. We can do it with larger numbers.

We could think about what about all the factor pairs for something like 16? Pause this video and see if you can think about that. Well, I'll set up a little table here to think about that, and so in this column, I'll put the first factor, and in this column, I'll put the second factor. The way I like to do it is I start at 1 and I keep working up, up to the number, to try to figure out all of the factors. So let's start with 1.

So 1 is definitely divisible into 16, and as long as you put a whole number here, it's going to be divisible by 1. What do I have to multiply by 1 to get to 16? Well, I'll have to multiply it by 16. So that's a factor pair right there: 1 and 16. Now, what about 2? Does 2 go into 16? Well sure, 2 times 8 is 16. So that's another factor pair: 2 times 8. We found another factor pair.

Now, what about 3? Does 3 go evenly into 16? Well, no. 3 times 5 is 15, and 3 times 6 is 18. So 3 doesn't go into 16, so 3 would not be a factor of 16. What about 4? Well, 4 times 4 is 16. So that's a factor pair there: 4 and 4. What about 5? Well, no. 5 times 2 is 10, 5 times 3 is 15, and 5 times 4 is 20. 5 does not go evenly into 16.

Same thing for 6. 6 times 2 is 12, and 6 times 3 is 18. It does not go evenly into 16. What about 7? 7 does not evenly go into 16. 7 times 2 is 14, and 7 times 3 is 21. What about 8? Well, we already know that 8 goes evenly into 16. You might be tempted to say, "Oh, there's another factor pair of 8 times 2."

But we already wrote that down. We just happened to say that 2 is the first factor and 8 is the second factor. But you could say it the other way around, so we don't have to then go to 8 times 2. Once you've gone halfway, you could be confident that you've already found all the factor pairs because then you could go to 9. 9 doesn't go into it. 10, 11, 12, 13, 14, 15, but then 16, of course, is divisible by 16, but we've already written that here in this factor pair.

So we have these three factor pairs: 1 and 16, 2 and 8, and 4 and 4.