Q: What are the factor combinations of the number 220,196?

 A:
Positive:   1 x 2201962 x 1100984 x 55049
Negative: -1 x -220196-2 x -110098-4 x -55049


How do I find the factor combinations of the number 220,196?

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 220,196, 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.

1 220,196
-1 -220,196

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 220,196.

Example:
1 x 220,196 = 220,196
and
-1 x -220,196 = 220,196
Notice both answers equal 220,196

With that explanation out of the way, let's continue. Next, we take the number 220,196 and divide it by 2:

220,196 ÷ 2 = 110,098

If the quotient is a whole number, then 2 and 110,098 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 110,098 220,196
-1 -2 -110,098 -220,196

Now, we try dividing 220,196 by 3:

220,196 ÷ 3 = 73,398.6667

If the quotient is a whole number, then 3 and 73,398.6667 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 2 110,098 220,196
-1 -2 -110,098 -220,196

Let's try dividing by 4:

220,196 ÷ 4 = 55,049

If the quotient is a whole number, then 4 and 55,049 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 55,049 110,098 220,196
-1 -2 -4 -55,049 -110,098 220,196
Keep dividing by the next highest number until you cannot divide anymore.

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

12455,049110,098220,196
-1-2-4-55,049-110,098-220,196

More Examples

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