Q: What are the factor combinations of the number 220,032,217?

 A:
Positive:   1 x 22003221719 x 11580643151 x 1457167271 x 811927283 x 7774992869 x 766935149 x 427335377 x 40921
Negative: -1 x -220032217-19 x -11580643-151 x -1457167-271 x -811927-283 x -777499-2869 x -76693-5149 x -42733-5377 x -40921


How do I find the factor combinations of the number 220,032,217?

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 220,032,217, 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.

1 220,032,217
-1 -220,032,217

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 220,032,217.

Example:
1 x 220,032,217 = 220,032,217
and
-1 x -220,032,217 = 220,032,217
Notice both answers equal 220,032,217

With that explanation out of the way, let's continue. Next, we take the number 220,032,217 and divide it by 2:

220,032,217 ÷ 2 = 110,016,108.5

If the quotient is a whole number, then 2 and 110,016,108.5 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:

1 220,032,217
-1 -220,032,217

Now, we try dividing 220,032,217 by 3:

220,032,217 ÷ 3 = 73,344,072.3333

If the quotient is a whole number, then 3 and 73,344,072.3333 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:

1 220,032,217
-1 -220,032,217

Let's try dividing by 4:

220,032,217 ÷ 4 = 55,008,054.25

If the quotient is a whole number, then 4 and 55,008,054.25 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:

1 220,032,217
-1 220,032,217
Keep dividing by the next highest number until you cannot divide anymore.

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

1191512712832,8695,1495,37740,92142,73376,693777,499811,9271,457,16711,580,643220,032,217
-1-19-151-271-283-2,869-5,149-5,377-40,921-42,733-76,693-777,499-811,927-1,457,167-11,580,643-220,032,217

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