Q: What are the factor combinations of the number 12,332,021?

 A:
Positive:   1 x 1233202113 x 94861717 x 72541341 x 300781221 x 55801533 x 23137697 x 176931361 x 9061
Negative: -1 x -12332021-13 x -948617-17 x -725413-41 x -300781-221 x -55801-533 x -23137-697 x -17693-1361 x -9061


How do I find the factor combinations of the number 12,332,021?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 12,332,021, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 12,332,021
-1 -12,332,021

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 12,332,021.

Example:
1 x 12,332,021 = 12,332,021
and
-1 x -12,332,021 = 12,332,021
Notice both answers equal 12,332,021

With that explanation out of the way, let's continue. Next, we take the number 12,332,021 and divide it by 2:

12,332,021 ÷ 2 = 6,166,010.5

If the quotient is a whole number, then 2 and 6,166,010.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 12,332,021
-1 -12,332,021

Now, we try dividing 12,332,021 by 3:

12,332,021 ÷ 3 = 4,110,673.6667

If the quotient is a whole number, then 3 and 4,110,673.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 12,332,021
-1 -12,332,021

Let's try dividing by 4:

12,332,021 ÷ 4 = 3,083,005.25

If the quotient is a whole number, then 4 and 3,083,005.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 12,332,021
-1 12,332,021
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

11317412215336971,3619,06117,69323,13755,801300,781725,413948,61712,332,021
-1-13-17-41-221-533-697-1,361-9,061-17,693-23,137-55,801-300,781-725,413-948,617-12,332,021

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