Q: What are the factor combinations of the number 12,688,625?

 A:
Positive:   1 x 126886255 x 253772525 x 50754583 x 152875125 x 101509415 x 305751223 x 103752075 x 6115
Negative: -1 x -12688625-5 x -2537725-25 x -507545-83 x -152875-125 x -101509-415 x -30575-1223 x -10375-2075 x -6115


How do I find the factor combinations of the number 12,688,625?

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 12,688,625, 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 12,688,625
-1 -12,688,625

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 12,688,625.

Example:
1 x 12,688,625 = 12,688,625
and
-1 x -12,688,625 = 12,688,625
Notice both answers equal 12,688,625

With that explanation out of the way, let's continue. Next, we take the number 12,688,625 and divide it by 2:

12,688,625 ÷ 2 = 6,344,312.5

If the quotient is a whole number, then 2 and 6,344,312.5 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 12,688,625
-1 -12,688,625

Now, we try dividing 12,688,625 by 3:

12,688,625 ÷ 3 = 4,229,541.6667

If the quotient is a whole number, then 3 and 4,229,541.6667 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 12,688,625
-1 -12,688,625

Let's try dividing by 4:

12,688,625 ÷ 4 = 3,172,156.25

If the quotient is a whole number, then 4 and 3,172,156.25 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 12,688,625
-1 12,688,625
Keep dividing by the next highest number until you cannot divide anymore.

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

1525831254151,2232,0756,11510,37530,575101,509152,875507,5452,537,72512,688,625
-1-5-25-83-125-415-1,223-2,075-6,115-10,375-30,575-101,509-152,875-507,545-2,537,725-12,688,625

More Examples

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