Q: What are the factor combinations of the number 223,225?

 A:
Positive:   1 x 2232255 x 4464525 x 8929
Negative: -1 x -223225-5 x -44645-25 x -8929


How do I find the factor combinations of the number 223,225?

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 223,225, 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.

1 223,225
-1 -223,225

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 223,225.

Example:
1 x 223,225 = 223,225
and
-1 x -223,225 = 223,225
Notice both answers equal 223,225

With that explanation out of the way, let's continue. Next, we take the number 223,225 and divide it by 2:

223,225 ÷ 2 = 111,612.5

If the quotient is a whole number, then 2 and 111,612.5 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:

1 223,225
-1 -223,225

Now, we try dividing 223,225 by 3:

223,225 ÷ 3 = 74,408.3333

If the quotient is a whole number, then 3 and 74,408.3333 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:

1 223,225
-1 -223,225

Let's try dividing by 4:

223,225 ÷ 4 = 55,806.25

If the quotient is a whole number, then 4 and 55,806.25 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:

1 223,225
-1 223,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15258,92944,645223,225
-1-5-25-8,929-44,645-223,225

More Examples

Here are some more numbers to try:

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