Q: What are the factor combinations of the number 225,563?

 A:
Positive:   1 x 22556313 x 17351
Negative: -1 x -225563-13 x -17351


How do I find the factor combinations of the number 225,563?

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 225,563, 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.

1 225,563
-1 -225,563

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 225,563.

Example:
1 x 225,563 = 225,563
and
-1 x -225,563 = 225,563
Notice both answers equal 225,563

With that explanation out of the way, let's continue. Next, we take the number 225,563 and divide it by 2:

225,563 ÷ 2 = 112,781.5

If the quotient is a whole number, then 2 and 112,781.5 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:

1 225,563
-1 -225,563

Now, we try dividing 225,563 by 3:

225,563 ÷ 3 = 75,187.6667

If the quotient is a whole number, then 3 and 75,187.6667 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:

1 225,563
-1 -225,563

Let's try dividing by 4:

225,563 ÷ 4 = 56,390.75

If the quotient is a whole number, then 4 and 56,390.75 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:

1 225,563
-1 225,563
Keep dividing by the next highest number until you cannot divide anymore.

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

11317,351225,563
-1-13-17,351-225,563

More Examples

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