Q: What are the factor combinations of the number 220,220,317?

 A:
Positive:   1 x 22022031719 x 11590543809 x 27221314327 x 15371
Negative: -1 x -220220317-19 x -11590543-809 x -272213-14327 x -15371


How do I find the factor combinations of the number 220,220,317?

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 220,220,317, 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.

1 220,220,317
-1 -220,220,317

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 220,220,317.

Example:
1 x 220,220,317 = 220,220,317
and
-1 x -220,220,317 = 220,220,317
Notice both answers equal 220,220,317

With that explanation out of the way, let's continue. Next, we take the number 220,220,317 and divide it by 2:

220,220,317 ÷ 2 = 110,110,158.5

If the quotient is a whole number, then 2 and 110,110,158.5 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:

1 220,220,317
-1 -220,220,317

Now, we try dividing 220,220,317 by 3:

220,220,317 ÷ 3 = 73,406,772.3333

If the quotient is a whole number, then 3 and 73,406,772.3333 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:

1 220,220,317
-1 -220,220,317

Let's try dividing by 4:

220,220,317 ÷ 4 = 55,055,079.25

If the quotient is a whole number, then 4 and 55,055,079.25 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:

1 220,220,317
-1 220,220,317
Keep dividing by the next highest number until you cannot divide anymore.

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

11980914,32715,371272,21311,590,543220,220,317
-1-19-809-14,327-15,371-272,213-11,590,543-220,220,317

More Examples

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