Q: What are the factor combinations of the number 12,402,131?

 A:
Positive:   1 x 124021317 x 177173341 x 30249179 x 156989287 x 43213547 x 22673553 x 224273239 x 3829
Negative: -1 x -12402131-7 x -1771733-41 x -302491-79 x -156989-287 x -43213-547 x -22673-553 x -22427-3239 x -3829


How do I find the factor combinations of the number 12,402,131?

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 12,402,131, 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 12,402,131
-1 -12,402,131

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 12,402,131.

Example:
1 x 12,402,131 = 12,402,131
and
-1 x -12,402,131 = 12,402,131
Notice both answers equal 12,402,131

With that explanation out of the way, let's continue. Next, we take the number 12,402,131 and divide it by 2:

12,402,131 ÷ 2 = 6,201,065.5

If the quotient is a whole number, then 2 and 6,201,065.5 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 12,402,131
-1 -12,402,131

Now, we try dividing 12,402,131 by 3:

12,402,131 ÷ 3 = 4,134,043.6667

If the quotient is a whole number, then 3 and 4,134,043.6667 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 12,402,131
-1 -12,402,131

Let's try dividing by 4:

12,402,131 ÷ 4 = 3,100,532.75

If the quotient is a whole number, then 4 and 3,100,532.75 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 12,402,131
-1 12,402,131
Keep dividing by the next highest number until you cannot divide anymore.

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

1741792875475533,2393,82922,42722,67343,213156,989302,4911,771,73312,402,131
-1-7-41-79-287-547-553-3,239-3,829-22,427-22,673-43,213-156,989-302,491-1,771,733-12,402,131

More Examples

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