Q: What are the factor combinations of the number 225,559?

 A:
Positive:   1 x 225559211 x 1069
Negative: -1 x -225559-211 x -1069


How do I find the factor combinations of the number 225,559?

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 225,559, 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.

1 225,559
-1 -225,559

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 225,559.

Example:
1 x 225,559 = 225,559
and
-1 x -225,559 = 225,559
Notice both answers equal 225,559

With that explanation out of the way, let's continue. Next, we take the number 225,559 and divide it by 2:

225,559 ÷ 2 = 112,779.5

If the quotient is a whole number, then 2 and 112,779.5 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:

1 225,559
-1 -225,559

Now, we try dividing 225,559 by 3:

225,559 ÷ 3 = 75,186.3333

If the quotient is a whole number, then 3 and 75,186.3333 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:

1 225,559
-1 -225,559

Let's try dividing by 4:

225,559 ÷ 4 = 56,389.75

If the quotient is a whole number, then 4 and 56,389.75 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:

1 225,559
-1 225,559
Keep dividing by the next highest number until you cannot divide anymore.

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

12111,069225,559
-1-211-1,069-225,559

More Examples

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