Q: What are the factor combinations of the number 12,625,925?

 A:
Positive:   1 x 126259255 x 252518513 x 97122525 x 50503753 x 23822565 x 194245265 x 47645325 x 38849689 x 18325733 x 172251325 x 95293445 x 3665
Negative: -1 x -12625925-5 x -2525185-13 x -971225-25 x -505037-53 x -238225-65 x -194245-265 x -47645-325 x -38849-689 x -18325-733 x -17225-1325 x -9529-3445 x -3665


How do I find the factor combinations of the number 12,625,925?

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 12,625,925, 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 12,625,925
-1 -12,625,925

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 12,625,925.

Example:
1 x 12,625,925 = 12,625,925
and
-1 x -12,625,925 = 12,625,925
Notice both answers equal 12,625,925

With that explanation out of the way, let's continue. Next, we take the number 12,625,925 and divide it by 2:

12,625,925 ÷ 2 = 6,312,962.5

If the quotient is a whole number, then 2 and 6,312,962.5 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 12,625,925
-1 -12,625,925

Now, we try dividing 12,625,925 by 3:

12,625,925 ÷ 3 = 4,208,641.6667

If the quotient is a whole number, then 3 and 4,208,641.6667 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 12,625,925
-1 -12,625,925

Let's try dividing by 4:

12,625,925 ÷ 4 = 3,156,481.25

If the quotient is a whole number, then 4 and 3,156,481.25 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 12,625,925
-1 12,625,925
Keep dividing by the next highest number until you cannot divide anymore.

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

15132553652653256897331,3253,4453,6659,52917,22518,32538,84947,645194,245238,225505,037971,2252,525,18512,625,925
-1-5-13-25-53-65-265-325-689-733-1,325-3,445-3,665-9,529-17,225-18,325-38,849-47,645-194,245-238,225-505,037-971,225-2,525,185-12,625,925

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