Q: What are the factor combinations of the number 90,125?

 A:
Positive:   1 x 901255 x 180257 x 1287525 x 360535 x 2575103 x 875125 x 721175 x 515
Negative: -1 x -90125-5 x -18025-7 x -12875-25 x -3605-35 x -2575-103 x -875-125 x -721-175 x -515


How do I find the factor combinations of the number 90,125?

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 90,125, 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 90,125
-1 -90,125

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 90,125.

Example:
1 x 90,125 = 90,125
and
-1 x -90,125 = 90,125
Notice both answers equal 90,125

With that explanation out of the way, let's continue. Next, we take the number 90,125 and divide it by 2:

90,125 ÷ 2 = 45,062.5

If the quotient is a whole number, then 2 and 45,062.5 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 90,125
-1 -90,125

Now, we try dividing 90,125 by 3:

90,125 ÷ 3 = 30,041.6667

If the quotient is a whole number, then 3 and 30,041.6667 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 90,125
-1 -90,125

Let's try dividing by 4:

90,125 ÷ 4 = 22,531.25

If the quotient is a whole number, then 4 and 22,531.25 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 90,125
-1 90,125
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351031251755157218752,5753,60512,87518,02590,125
-1-5-7-25-35-103-125-175-515-721-875-2,575-3,605-12,875-18,025-90,125

More Examples

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