Q: What are the factor combinations of the number 403,525?

 A:
Positive:   1 x 4035255 x 8070525 x 16141
Negative: -1 x -403525-5 x -80705-25 x -16141


How do I find the factor combinations of the number 403,525?

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 403,525, 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.

1 403,525
-1 -403,525

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 403,525.

Example:
1 x 403,525 = 403,525
and
-1 x -403,525 = 403,525
Notice both answers equal 403,525

With that explanation out of the way, let's continue. Next, we take the number 403,525 and divide it by 2:

403,525 ÷ 2 = 201,762.5

If the quotient is a whole number, then 2 and 201,762.5 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:

1 403,525
-1 -403,525

Now, we try dividing 403,525 by 3:

403,525 ÷ 3 = 134,508.3333

If the quotient is a whole number, then 3 and 134,508.3333 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:

1 403,525
-1 -403,525

Let's try dividing by 4:

403,525 ÷ 4 = 100,881.25

If the quotient is a whole number, then 4 and 100,881.25 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:

1 403,525
-1 403,525
Keep dividing by the next highest number until you cannot divide anymore.

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

152516,14180,705403,525
-1-5-25-16,141-80,705-403,525

More Examples

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