Q: What are the factor combinations of the number 221,156,723?

 A:
Positive:   1 x 22115672317 x 1300921989 x 2484907313 x 706571467 x 4735691513 x 1461715321 x 415637939 x 27857
Negative: -1 x -221156723-17 x -13009219-89 x -2484907-313 x -706571-467 x -473569-1513 x -146171-5321 x -41563-7939 x -27857


How do I find the factor combinations of the number 221,156,723?

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 221,156,723, 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.

1 221,156,723
-1 -221,156,723

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 221,156,723.

Example:
1 x 221,156,723 = 221,156,723
and
-1 x -221,156,723 = 221,156,723
Notice both answers equal 221,156,723

With that explanation out of the way, let's continue. Next, we take the number 221,156,723 and divide it by 2:

221,156,723 ÷ 2 = 110,578,361.5

If the quotient is a whole number, then 2 and 110,578,361.5 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:

1 221,156,723
-1 -221,156,723

Now, we try dividing 221,156,723 by 3:

221,156,723 ÷ 3 = 73,718,907.6667

If the quotient is a whole number, then 3 and 73,718,907.6667 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:

1 221,156,723
-1 -221,156,723

Let's try dividing by 4:

221,156,723 ÷ 4 = 55,289,180.75

If the quotient is a whole number, then 4 and 55,289,180.75 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:

1 221,156,723
-1 221,156,723
Keep dividing by the next highest number until you cannot divide anymore.

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

117893134671,5135,3217,93927,85741,563146,171473,569706,5712,484,90713,009,219221,156,723
-1-17-89-313-467-1,513-5,321-7,939-27,857-41,563-146,171-473,569-706,571-2,484,907-13,009,219-221,156,723

More Examples

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