WEBVTT

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Find all of the factors
of 120.

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Or another way to think about
it, find all of the whole

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numbers that 120 is
divisible by.

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So the first one, that's
maybe obvious.

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All whole numbers are
divisible by 1.

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So we could write 120 is equal
to is to 1 times 120.

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So let's write a factors
list over here.

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So this is going to be our
factors list over here.

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So we just found two factors.

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We said, well, is it
divisible by 1?

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Well, every whole number
is divisible by 1.

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This is a whole number, so 1
is a factor at the low end.

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1 is a factor.

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That's its actual smallest
factor, and its

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largest factor is 120.

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You can't have something larger
than 120 dividing

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evenly into 120.

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121 will not go into 120.

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So the largest factor
on our factors list

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is going to be 120.

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Now let's think about others.

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Let's think about whether
is 2 divisible into 120?

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So there's 120 equals
2 times something?

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Well, when you look here,
maybe you immediately

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recognize that 120 is
an even number.

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It's ones place is a 0.

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As as long as its ones place is
a 0, 2, 4, 6 or 8, as long

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as it's an even number, the
whole number is even and the

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whole number is divisible
by 2.

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And to figure out what you have
to multiply by 2 to get

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120, well, you can think of 120
as 12 times 10, or another

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way to think about it,
it's 2 times 6 times

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10, or 2 times 60.

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You could divide it
out if you want.

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You could say, OK,
2 goes into 120.

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2 goes into 1 no times.

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2 goes into 12 six times.

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6 times 2 is 12.

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Subtract.

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You get 0.

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Bring down the 0.

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2 goes into 0 zero times.

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0 times 2 is 0, and you get no
remainder there, so it goes

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sixty times.

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So we have two more factors
right here.

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So we have the factors.

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So we've established the next
lowest one is 2, and the next

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highest factor, if we're
starting from the large end,

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is going to be 60.

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Now let's think about three.

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Is 120 equal to 3
times something?

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Well, we could just try to test
and divide it from the

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get go, but hopefully,
you already know the

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divisibility rule.

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To figure out if something is
divisible by 3, you add up its

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digits, and if the
sum is divisible

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by 3, we're in business.

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So if you take 120-- let
me do it over here.

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1 plus 2 plus 0, well, that's
equal to 1 plus 2 is 3 plus 0

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is 3, and 3 is definitely
divisible by 3.

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So 120 is going to be
divisible by 3.

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To figure what that number that
you have to multiply by 3

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is, you could do it
in your head.

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You could say, well, 3 goes into
12 four times, and then

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you-- well, let me just do it
out, just in case, just for

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those of you who want to
see it worked out.

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3 goes into 12 four times.

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4 times 3 is 12.

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You subtract.

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You're left with nothing here.

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You bring down this 0.

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3 goes into 0 zero times.

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0 times 3 is 0.

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Nothing left over.

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So it goes into it
forty times.

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And the way to think of it in
your head is this is the same

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thing as 12 times 10.

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12 divided by 3 is 4, but this
is going to be 4 times 10,

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because you have that
10 left over.

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Whatever works for you.

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Or you can just ignore the 0,
divide by 3, you get a 4, and

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then put the 0 back there.

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Whatever works.

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So we have two more factors.

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At the low end, we have 3, and
at the high end, we have a 40.

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Now, let's see if 4 divisible
into 120.

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Now we saw the divisibility
rule for 4 is you ignore

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everything beyond the tens
places and you just look at

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the last two digits.

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So if we're going to to think
about whether 4 is divisible,

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you just look at the
last two digits.

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The last two digits are 20.

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20 is definitely divisible
by 4, so 120 will be

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divisible by 4.

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4 is going to be a factor.

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And to figure out what we have
to multiply 4 by to get 120,

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you could do it in your head.

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You could say 12 divided
by 4 is 3, so 120

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divided by 4 is 30.

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So we have two more
factors: 4 and 30.

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And you could work this out in
long division if you want to

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make sure that this works out,
so let's keep going.

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And then we have 120 is equal
to-- is 5 a factor?

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Is 5 times something
equal to 120?

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Well, you can't do that simple--
well, first of all,

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we could just test
is it divisible?

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And 120 ends with a 0.

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If you end with a 0 or a 5,
you are divisible by 5.

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So 5 definitely goes into it.

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Let's figure out
how many times.

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So 5 goes into 120.

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It doesn't go into 1.

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It goes into 12 two times.

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2 times 5 is 10.

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Subtract.

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You get 2.

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Bring down the 0.

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5 goes into 20 four times.

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4 times 5 is 20, and then you
subtract, and you have no left

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over, as we expect, because
it should go in evenly.

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This number ends with
a 0 or a 5.

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Let me delete all of this so we
can have our scratch space

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to work with later on.

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So 5 times 24 is also equal
to 120, we have two more

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factors: 5 and 24.

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Let me clear up some space here
because I think we're

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going to be dealing with
a lot of factors.

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So let me move this
right here.

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Let me cut it and then let me
paste it and move this over

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here so we have more space
for our factors.

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So we have 5 and 24.

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Let's move on to 6.

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So 120 is equal to
6 times what?

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Now, to be divisible by
6, you have to be

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divisible by 2 and 3.

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Now, we know that we're already
divisible by 2 and 3,

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so we're definitely going to
be divisible by 6, and you

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should hopefully be able to
do this one in your head.

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5 was a little bit harder to do
in your head. but 120, you

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could say, well, 12 divided by 6
is 2, and then you have that

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0 there, so 120 divided
by 6 would be 20.

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And you could work it out in
long division if you like.

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So 6 times 20 are two
more factors.

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Now let's think about 7.

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Let's think about 7 here.

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7 is a very bizarre number, and
just to test it, you could

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think of other ways to do it.

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Let's just try to divide
7 into 120.

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7 doesn't go into 1.

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It goes into 12 one time.

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1 times 7 is 7.

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You subtract.

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12 minus 7 is 5.

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Bring down the 0.

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7 times 7 is 49, so it goes
into it seven times.

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7 times 7 is 49.

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Subtract.

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You have a remainder, so it
does not divide evenly.

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So 7 does not work.

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Now let's think about 8.

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Let's think about
whether 8 works.

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Let's think about 8.

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I'll do the same process.

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Let's take 8 into 120.

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Let's just work it out.

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And just as a little bit
of a hint-- well, I'll

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just work it out.

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8 goes into 12-- it doesn't
go into 1, so it

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goes into 12 one time.

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1 times 8 is 8.

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Subtract there.

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12 minus 8 is 4.

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Bring down the 0.

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8 goes into 40 five times.

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5 times 8 is 40, and you're left
with no remainder, so it

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goes evenly.

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So 120-- let me get
rid of that.

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120 is equal to 8 times 15, so
let's add that to our factor

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list. We now have an 8
and now we have a 15.

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Now, is it divisible by 9?

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Is 120 divisible by 9?

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To test that out, you just
add up the digits.

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1 plus 2 plus 0 is equal to 3.

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Well, that'll satisfy our 3
divisibility rule, but 3 is

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not divisible by 9, so our
number will not be

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divisible by 9.

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So 9 will not work out.

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9 does not work out.

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So let's move on to 10.

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Well, this is pretty
straightforward.

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It ends in 0, so we will
be divisible by 10.

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So let me write that down.

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120 is equal to 10 times--
and this is pretty

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straightforward-- 10 times 12.

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This is exactly what 120 is.

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It's 10 times 12, so let's
write those factors down.

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10 and 12.

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And then we have one
number left.

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We have 11.

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We don't have to go above 11,
because we already went

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through 12, and we know that
there aren't any factors above

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that, because we were going in
descending order, so we've

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really filled in all the gaps.

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You could try 11.

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We could try it by hand,
if you like.

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11 goes into 120-- now you know,
if with you know your

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multiplication tables through
11, that this won't work, but

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I'll just show you.

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11 goes into 12 one time.

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1 times 11 is 11.

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Subtract.

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1, bring down the 0.

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11 goes into 10 zero times.

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0 times 11 is 0.

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you're left with a
remainder of 10.

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So 11 goes into 20 ten times
with a remainder of 10.

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It definitely does
not go in evenly.

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So we have all of our factors
here: 1, 2, 3, 4, 5, 6, 8, 10,

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12, 15, 20, 24, 30,
40, 60 and 120.

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And we're done!

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