Divisibility Intuition

Example of working on KA Divisibility Module: http://www.khanacademy.org/math/arithmetic/factors-multiples/e/divisibility_intuition

[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.