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Studying for a test? Prepare with this lesson on Factors and multiples.
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SAL KHAN: I'm here with our exercise guru, Ben Eater-- BEN EATER: Hi, Sal. SAL KHAN: --who made this exercise, and now we're going to try to work through it. So let's see. It says what are the factors of 9? You can re-size this box with 9 dots-- the box has 9 dots-- to help you find the factors. BEN EATER: So what you're looking at, is you've got these 9 dots on the screen. And right now, there are just 1 row of 9 dots. And if you grab that little thing on the right side of the box and move that around to the left-- SAL KHAN: Oh, that's neat. BEN EATER: --you still have 9 dots, but they're arranged differently. SAL KHAN: I see. BEN EATER: And so what you can see is, try to get them so you have the same number in each row. SAL KHAN: I see, so this one. So if you have-- let's see, not the same number. BEN EATER: There you go. SAL KHAN: Oh, 3 there. And so you could get to 9 by literally multiplying 3 rows times 3 columns. BEN EATER: That's right. SAL KHAN: And you get to 9. BEN EATER: So 3 is a factor. SAL KHAN: And then we would write that in this box right over here. BEN EATER: Mm-hm. SAL KHAN: So we'd write 3-- do we have to write 3 twice, because we have-- or is just writing 3 once-- BEN EATER: 3 is the factor-- SAL KHAN: 3 is a factor. BEN EATER: --so you just put it once. SAL KHAN: We don't have to write it. If we wrote it twice would it be wrong? BEN EATER: Uh-huh, yes, actually. SAL KHAN: It would? OK, so-- BEN EATER: We do mark that wrong. SAL KHAN: --you actually do mark that wrong. OK, so there's 3 and 3. But there was also, right when you started, you had 9 and 1. BEN EATER: That's right. Both of those are factors. SAL KHAN: And I don't have to write these in any special order? BEN EATER: No, no. SAL KHAN: 1 and 9. BEN EATER: Just got to get them all. SAL KHAN: And I believe that's all there is. And we could look at the other ones, and we can see, look 2 and 8 definitely-- BEN EATER: No. SAL KHAN: No, that's not working out. It's interesting for people to think about why these aren't working out. BEN EATER: Right. Yeah, you can't divide 2 into 9. SAL KHAN: And this just gets us to 1 and 9 again, and we don't want to repeat it. BEN EATER: Those are the same factors. SAL KHAN: Exactly. So let's check our answer. Let's see how we're doing. BEN EATER: OK. SAL KHAN: Let's see. There we go. We got it all right. Let's do one more. BEN EATER: OK. SAL KHAN: Let's do one more. Correct. The next question. You can resize this box with 16 dots to help you find the factor. It's 1 and 16. BEN EATER: 1 and 16 are factors, sure. SAL KHAN: So me write those. BEN EATER: Those are all its factors. SAL KHAN: So 1 and 16. So let's play with this box here. That's not working. That's not working. So I'm trying to figure out-- so this is essentially going 2 times-- 2 might be a factor if I could just-- oh look, it is. BEN EATER: There it is, yeah. 2 is a factor SAL KHAN: 2 is a factor. BEN EATER: And so is 8. SAL KHAN: Exactly, exactly. 2 rows of 8 works. And so we could say 2 and 8 are factors. BEN EATER: And if you think about it, 2 and 8 both divide into 16. SAL KHAN: Absolutely. BEN EATER: 2 divides eight times. SAL KHAN: Yes. BEN EATER: Or 8 divides two times. SAL KHAN: Yes, you can that. You can construct. BEN EATER: Right. SAL KHAN: 16 dots, you can divide them into 2 groups of 8. BEN EATER: That's right. SAL KHAN: And I suspect also 8 groups of 2. BEN EATER: Well, you can see that. SAL KHAN: Let's see, so that's 2 groups of 8, really, or 2 rows of 8. Let's see, or oh, look at that. 4 times 4. BEN EATER: 4 times 4. SAL KHAN: And I'll just write the 4 once. BEN EATER: So 4 is a factor. SAL KHAN: 4 is a factor. And then I can-- and I've probably-- well, I've already gotten 8 and 2. BEN EATER: Already got that. SAL KHAN: Now I have 8 groups of 2 instead of 2 groups of 8, but they're still both factors. Then you go back to 16 and 1. BEN EATER: That's right. SAL KHAN: So I think we're done. BEN EATER: I think so. SAL KHAN: Let's check our answer. Oh-- BEN EATER: Very good. SAL KHAN: --very good, very good. Well, thank you. That was fun. BEN EATER: Thank you. SAL KHAN: This was very neat, very fun to play with. BEN EATER: Well, thanks.