Q: What are the factor combinations of the number 90,339,625?

 A:
Positive:   1 x 903396255 x 1806792525 x 3613585125 x 722717313 x 2886251565 x 577252309 x 391257825 x 11545
Negative: -1 x -90339625-5 x -18067925-25 x -3613585-125 x -722717-313 x -288625-1565 x -57725-2309 x -39125-7825 x -11545


How do I find the factor combinations of the number 90,339,625?

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 90,339,625, 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 90,339,625
-1 -90,339,625

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 90,339,625.

Example:
1 x 90,339,625 = 90,339,625
and
-1 x -90,339,625 = 90,339,625
Notice both answers equal 90,339,625

With that explanation out of the way, let's continue. Next, we take the number 90,339,625 and divide it by 2:

90,339,625 ÷ 2 = 45,169,812.5

If the quotient is a whole number, then 2 and 45,169,812.5 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 90,339,625
-1 -90,339,625

Now, we try dividing 90,339,625 by 3:

90,339,625 ÷ 3 = 30,113,208.3333

If the quotient is a whole number, then 3 and 30,113,208.3333 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 90,339,625
-1 -90,339,625

Let's try dividing by 4:

90,339,625 ÷ 4 = 22,584,906.25

If the quotient is a whole number, then 4 and 22,584,906.25 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 90,339,625
-1 90,339,625
Keep dividing by the next highest number until you cannot divide anymore.

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

15251253131,5652,3097,82511,54539,12557,725288,625722,7173,613,58518,067,92590,339,625
-1-5-25-125-313-1,565-2,309-7,825-11,545-39,125-57,725-288,625-722,717-3,613,585-18,067,925-90,339,625

More Examples

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