5-4-81 factoring
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When doing this kind of problem, we're going to start by
multiplying the 18 and the 14 and we're going to get 252 from
the 252.
We're going to have 1:00 and 2:52 two and 126 four and 63.
Now 250 two, 2 + 5 + 2 is 9, so we know that three goes into
that.
So 3 into 252 three goes into 25 eight times, so 84 and 84 is
even.
So if I took a 2 out of 84, I'd get 6 * 42.
If I took a two out again, I'd get 12 * 21, and then I can't
take a two out.
Now divisibility test for 9 is the same for three.
2 + 5 + 2 is 9, so I know nine goes evenly into this.
So 99 goes into 25 two times, 18 with seven leftover.
Nine goes into 72 eight times.
We could pull A2 out of here and we would get 18 * 14.
Now, the fact that we have a 14 actually tells us seven can go
in.
Also.
Five's not going to because it didn't end in a zero or five.
But if any of these are divisible by 7 along the way,
then 7's got to go into the original.
So let's move 6 and 42 up.
So if I take a 7 out of 14 and put 2 * 18, that's 36 and I want
the sum to be a -33.
So I have 12345 doesn't go because zero or 5678 won't go
because we didn't have four times an even #9's here.
10 can't go because we didn't have a zero at the end.
11's not going to go.
We have 1213 won't go.
1415's not going to go because five didn't.
16 won't go because eight didn't.
So these are all of our possibilities.
So we want a sum.
So 253, 1/28, 87 hands on top of my numbers while I'm writing
6748, 43, 3733 and 32, we want -33 so we're going to use this
12 and 21 and negatives for each of them.
So if I say a -, 12 eighteenths W * a -, 21 eighteenths W, we're
going to simplify it.
So we're going to get a -, 2/3 W and a -, 3 goes into both those,
so 76 W and then we just pull the denominator out as the
leading coefficient.
So this is factoring into three a -, 2 W times six a -, 7 W.