Q: What are the factor combinations of the number 221,002,117?

 A:
Positive:   1 x 2210021177 x 31571731
Negative: -1 x -221002117-7 x -31571731


How do I find the factor combinations of the number 221,002,117?

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 221,002,117, 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.

1 221,002,117
-1 -221,002,117

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 221,002,117.

Example:
1 x 221,002,117 = 221,002,117
and
-1 x -221,002,117 = 221,002,117
Notice both answers equal 221,002,117

With that explanation out of the way, let's continue. Next, we take the number 221,002,117 and divide it by 2:

221,002,117 ÷ 2 = 110,501,058.5

If the quotient is a whole number, then 2 and 110,501,058.5 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:

1 221,002,117
-1 -221,002,117

Now, we try dividing 221,002,117 by 3:

221,002,117 ÷ 3 = 73,667,372.3333

If the quotient is a whole number, then 3 and 73,667,372.3333 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:

1 221,002,117
-1 -221,002,117

Let's try dividing by 4:

221,002,117 ÷ 4 = 55,250,529.25

If the quotient is a whole number, then 4 and 55,250,529.25 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:

1 221,002,117
-1 221,002,117
Keep dividing by the next highest number until you cannot divide anymore.

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

1731,571,731221,002,117
-1-7-31,571,731-221,002,117

More Examples

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