Q: What are the factor combinations of the number 12,111,107?

 A:
Positive:   1 x 1211110759 x 205273233 x 51979881 x 13747
Negative: -1 x -12111107-59 x -205273-233 x -51979-881 x -13747


How do I find the factor combinations of the number 12,111,107?

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 12,111,107, 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 12,111,107
-1 -12,111,107

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 12,111,107.

Example:
1 x 12,111,107 = 12,111,107
and
-1 x -12,111,107 = 12,111,107
Notice both answers equal 12,111,107

With that explanation out of the way, let's continue. Next, we take the number 12,111,107 and divide it by 2:

12,111,107 ÷ 2 = 6,055,553.5

If the quotient is a whole number, then 2 and 6,055,553.5 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 12,111,107
-1 -12,111,107

Now, we try dividing 12,111,107 by 3:

12,111,107 ÷ 3 = 4,037,035.6667

If the quotient is a whole number, then 3 and 4,037,035.6667 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 12,111,107
-1 -12,111,107

Let's try dividing by 4:

12,111,107 ÷ 4 = 3,027,776.75

If the quotient is a whole number, then 4 and 3,027,776.75 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 12,111,107
-1 12,111,107
Keep dividing by the next highest number until you cannot divide anymore.

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

15923388113,74751,979205,27312,111,107
-1-59-233-881-13,747-51,979-205,273-12,111,107

More Examples

Here are some more numbers to try:

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