Q: What are the factor combinations of the number 108,425?

 A:
Positive:   1 x 1084255 x 2168525 x 4337
Negative: -1 x -108425-5 x -21685-25 x -4337


How do I find the factor combinations of the number 108,425?

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 108,425, 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.

1 108,425
-1 -108,425

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 108,425.

Example:
1 x 108,425 = 108,425
and
-1 x -108,425 = 108,425
Notice both answers equal 108,425

With that explanation out of the way, let's continue. Next, we take the number 108,425 and divide it by 2:

108,425 ÷ 2 = 54,212.5

If the quotient is a whole number, then 2 and 54,212.5 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:

1 108,425
-1 -108,425

Now, we try dividing 108,425 by 3:

108,425 ÷ 3 = 36,141.6667

If the quotient is a whole number, then 3 and 36,141.6667 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:

1 108,425
-1 -108,425

Let's try dividing by 4:

108,425 ÷ 4 = 27,106.25

If the quotient is a whole number, then 4 and 27,106.25 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:

1 108,425
-1 108,425
Keep dividing by the next highest number until you cannot divide anymore.

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

15254,33721,685108,425
-1-5-25-4,337-21,685-108,425

More Examples

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