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Understanding factor pairs

Use multiplication and an understanding of area to identify factor pairs for 6 and 16. Created by Sal Khan.

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Video transcript

- 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 six, I could multiply two times three to get six and so we would say that two and three are factors of six. In fact we would also say that two and three is a factor pair for six 'cause when I multiply those two I can get six. 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 six? Well you could do it if it's two units by three units. So it could look something like this, I'll just hand draw it. So let's say it has, so let's say our rectangle looks like this. So it has two rows and then three columns and lets 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 it's 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 and 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 and the way I like to do it is I start at one and I keep working up, up to the number, to try to figure out all of the factors. So let's start with one. So one is definitely divisible into 16 and as long as you put a whole number here it's going to be divisible by one and we don't have to multiply by one to get to 16, we'll have to multiply it by 16 so that's a factor pair right there, one and 16. Now what about two? Does two go into 16? Well sure, two times eight is 16 so that's another factor pair. Two times eight. We found another factor pair. Now what about three? Does three go evenly into 16? Well no, three times five is 15 and three times six is 18 so three doesn't go into 16 so three would not be a factor of 16. What about four? Well four times four is 16 so that's a factor pair there. Four and four. What about five? Well no, five times two is 10, five times three is 15, five times four is 20. Five does not go evenly into 16. Same thing for six, six times two is 12, six times three is 18, does not go evenly into 16. What about seven? Seven does not evenly go into 16. Seven times two is 14, seven times three is 21. What about eight? Well we already know that eight goes evenly into 16, you might be tempted to say oh there's another factor pair of eight times two but we already wrote that down. We just happened to say that two is the first factor and eight is the second factor but you could say it the other way around so we don't have to then go to eight times two. And once you've gone half way you can be confident that you've already found all the factor pairs because then you could go to nine, nine 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, one and 16, two and eight and four and four.