Q: What are the factor combinations of the number 12,513,235?

 A:
Positive:   1 x 125132355 x 25026477 x 178760535 x 35752161 x 205135305 x 41027427 x 293052135 x 5861
Negative: -1 x -12513235-5 x -2502647-7 x -1787605-35 x -357521-61 x -205135-305 x -41027-427 x -29305-2135 x -5861


How do I find the factor combinations of the number 12,513,235?

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 12,513,235, 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 12,513,235
-1 -12,513,235

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 12,513,235.

Example:
1 x 12,513,235 = 12,513,235
and
-1 x -12,513,235 = 12,513,235
Notice both answers equal 12,513,235

With that explanation out of the way, let's continue. Next, we take the number 12,513,235 and divide it by 2:

12,513,235 ÷ 2 = 6,256,617.5

If the quotient is a whole number, then 2 and 6,256,617.5 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 12,513,235
-1 -12,513,235

Now, we try dividing 12,513,235 by 3:

12,513,235 ÷ 3 = 4,171,078.3333

If the quotient is a whole number, then 3 and 4,171,078.3333 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 12,513,235
-1 -12,513,235

Let's try dividing by 4:

12,513,235 ÷ 4 = 3,128,308.75

If the quotient is a whole number, then 4 and 3,128,308.75 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 12,513,235
-1 12,513,235
Keep dividing by the next highest number until you cannot divide anymore.

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

15735613054272,1355,86129,30541,027205,135357,5211,787,6052,502,64712,513,235
-1-5-7-35-61-305-427-2,135-5,861-29,305-41,027-205,135-357,521-1,787,605-2,502,647-12,513,235

More Examples

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