Q: What are the factor combinations of the number 12,624,125?

 A:
Positive:   1 x 126241255 x 252482523 x 54887525 x 504965115 x 109775125 x 100993575 x 219552875 x 4391
Negative: -1 x -12624125-5 x -2524825-23 x -548875-25 x -504965-115 x -109775-125 x -100993-575 x -21955-2875 x -4391


How do I find the factor combinations of the number 12,624,125?

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 12,624,125, 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 12,624,125
-1 -12,624,125

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 12,624,125.

Example:
1 x 12,624,125 = 12,624,125
and
-1 x -12,624,125 = 12,624,125
Notice both answers equal 12,624,125

With that explanation out of the way, let's continue. Next, we take the number 12,624,125 and divide it by 2:

12,624,125 ÷ 2 = 6,312,062.5

If the quotient is a whole number, then 2 and 6,312,062.5 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 12,624,125
-1 -12,624,125

Now, we try dividing 12,624,125 by 3:

12,624,125 ÷ 3 = 4,208,041.6667

If the quotient is a whole number, then 3 and 4,208,041.6667 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 12,624,125
-1 -12,624,125

Let's try dividing by 4:

12,624,125 ÷ 4 = 3,156,031.25

If the quotient is a whole number, then 4 and 3,156,031.25 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 12,624,125
-1 12,624,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1523251151255752,8754,39121,955100,993109,775504,965548,8752,524,82512,624,125
-1-5-23-25-115-125-575-2,875-4,391-21,955-100,993-109,775-504,965-548,875-2,524,825-12,624,125

More Examples

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