Q: What are the factor combinations of the number 12,375,965?

 A:
Positive:   1 x 123759655 x 24751937 x 176799535 x 353599103 x 120155515 x 24031721 x 171653433 x 3605
Negative: -1 x -12375965-5 x -2475193-7 x -1767995-35 x -353599-103 x -120155-515 x -24031-721 x -17165-3433 x -3605


How do I find the factor combinations of the number 12,375,965?

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 12,375,965, 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 12,375,965
-1 -12,375,965

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 12,375,965.

Example:
1 x 12,375,965 = 12,375,965
and
-1 x -12,375,965 = 12,375,965
Notice both answers equal 12,375,965

With that explanation out of the way, let's continue. Next, we take the number 12,375,965 and divide it by 2:

12,375,965 ÷ 2 = 6,187,982.5

If the quotient is a whole number, then 2 and 6,187,982.5 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 12,375,965
-1 -12,375,965

Now, we try dividing 12,375,965 by 3:

12,375,965 ÷ 3 = 4,125,321.6667

If the quotient is a whole number, then 3 and 4,125,321.6667 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 12,375,965
-1 -12,375,965

Let's try dividing by 4:

12,375,965 ÷ 4 = 3,093,991.25

If the quotient is a whole number, then 4 and 3,093,991.25 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 12,375,965
-1 12,375,965
Keep dividing by the next highest number until you cannot divide anymore.

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

157351035157213,4333,60517,16524,031120,155353,5991,767,9952,475,19312,375,965
-1-5-7-35-103-515-721-3,433-3,605-17,165-24,031-120,155-353,599-1,767,995-2,475,193-12,375,965

More Examples

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