Q: What are the factor combinations of the number 220,123,021?

 A:
Positive:   1 x 22012302117 x 1294841329 x 7590449493 x 446497521 x 422501857 x 2568538857 x 2485314569 x 15109
Negative: -1 x -220123021-17 x -12948413-29 x -7590449-493 x -446497-521 x -422501-857 x -256853-8857 x -24853-14569 x -15109


How do I find the factor combinations of the number 220,123,021?

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 220,123,021, 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.

1 220,123,021
-1 -220,123,021

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 220,123,021.

Example:
1 x 220,123,021 = 220,123,021
and
-1 x -220,123,021 = 220,123,021
Notice both answers equal 220,123,021

With that explanation out of the way, let's continue. Next, we take the number 220,123,021 and divide it by 2:

220,123,021 ÷ 2 = 110,061,510.5

If the quotient is a whole number, then 2 and 110,061,510.5 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:

1 220,123,021
-1 -220,123,021

Now, we try dividing 220,123,021 by 3:

220,123,021 ÷ 3 = 73,374,340.3333

If the quotient is a whole number, then 3 and 73,374,340.3333 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:

1 220,123,021
-1 -220,123,021

Let's try dividing by 4:

220,123,021 ÷ 4 = 55,030,755.25

If the quotient is a whole number, then 4 and 55,030,755.25 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:

1 220,123,021
-1 220,123,021
Keep dividing by the next highest number until you cannot divide anymore.

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

117294935218578,85714,56915,10924,853256,853422,501446,4977,590,44912,948,413220,123,021
-1-17-29-493-521-857-8,857-14,569-15,109-24,853-256,853-422,501-446,497-7,590,449-12,948,413-220,123,021

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