Divisibility and factors
Divisibility Intuition Example of Sal working on KA Divisibility Module: http://www.khanacademy.org/math/arithmetic/factors-multiples/e/divisibility_intuition
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- [Sal] I'm here with our exercise guru, Ben Eater,
- [Ben] Hi Sal
- [Sal] 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 resize this box with 9 dots",
- the box has 9 dots
- "to help you find the factors"
- [Ben] Yeah, so what you're looking at,
- you've got, you've got these 9 dots on the screen
- and right now they're just one 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] Oh, that's neat!
- [Ben] you still have 9 dots, but they're arranged differently
- [Sal] I see
- [Ben] And so, what you can see is,
- try to go get them so you have the
- same number in each row
- [Sal] I see, so this one, so if you have
- let's see, not the same number
- Oh, 3, right there!
- So you could get to 9 by literally multiplying 3 rows times 3 columns
- [Ben] That's right.
- [Sal] and you get to 9
- [Ben] So 3 is a factor
- [Sal] So 3, and we'd write that in this box over here
- Do we have to write 3 twice? because we have...
- or is just writing 3 once?
- [Ben] 3 is a factor
- (overlapping) [Sal] 3 is a factor, we don't have to write [Ben] so you just put it once.
- [Sal] If we wrote it twice, would it be wrong?
- [Ben] Yes actually. We do mark that wrong.
- [Sal] 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] That's right, those are factors.
- [Sal] and I dont have to write them in any special order?
- [Ben] no, no. gotta get them all.
- [Sal] And I belive that's all there is
- And we can look at the other ones
- And we could see, look 2 and 8, definitely that's not working out
- and it's interesting for people to think
- about why these aren't working out
- [Ben] Right, yeah, you can't divide two into nine
- [Sal] Yes, yeah, yeah, yeah
- That's pretty...
- And that just gets us to 1 and 9 again
- And we don't want to repeat it.
- [Ben] Those are the same factors
- [Sal] So let's check our answer, let's see how we're doing.
- There we go! We got it all right.
- Let's do one more [Ben] Ok
- [Sal] Let's do one more. Correct. Next question.
- You can resize this box with 16 dots to help you find the factors
- So 1 I'll just, 1 and 16 are factors
- [Ben] 1 and 16 are factors, sure
- Those are always factors
- [Sal] Let me write those: 1 and 16
- So let's play with this box here
- So, yeah, I know, that's not working
- That's not working
- So I'm trying to figure out
- So this is essentiall going 2 times...
- 2 might be a factor, if I could just
- Oh, look it is!
- [Ben] There it is. Two is a factor.
- [Sal] Exactly, 2 rows of 8 works
- So we can say 2 and 8 are factors.
- [Ben] And if you think of it 2 and 8 both divide into 16
- [Sal] Absolutely
- [Ben] 2 divides 8 times or 8 divides 2 times
- [Sal] Yes. You can see that.
- You can construct
- 16 dots, you can divide them into 2 groups of 8
- and I suspect also 8 groups of 2
- [Ben] Well, you can see that
- [Sal] Let's see. So that's two groups of 8
- or two rows of 8
- let's see, 4 - Oh, look at that! 4 times 4
- [Ben] 4 times 4
- [Sal] And I'll just write the 4 once
- [Ben] 4 is a factor
- [Sal] 4 is a factor
- and then I can
- and I've probably
- I've already gotten 8 and 2
- Now I've got 8 groups of 2 instead of two groups of 8
- but they're still both factors
- and you go back to 16 and 1
- So, I think we're done.
- [Ben] I think so!
- [Sal] Let's check our answer.
- [Both] Very good!
- [Sal] Well, thank you. That was fun.
- [Ben] Thank you
- [Sal] This was very neat. Very fun to play with.
- [Ben] Oh, thanks.
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