Q: What are the factor combinations of the number 521,553,221?

 A:
Positive:   1 x 5215532217 x 7450760323 x 2267622737 x 14096033161 x 3239461259 x 2013719851 x 6128715957 x 87553
Negative: -1 x -521553221-7 x -74507603-23 x -22676227-37 x -14096033-161 x -3239461-259 x -2013719-851 x -612871-5957 x -87553


How do I find the factor combinations of the number 521,553,221?

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 521,553,221, 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.

1 521,553,221
-1 -521,553,221

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 521,553,221.

Example:
1 x 521,553,221 = 521,553,221
and
-1 x -521,553,221 = 521,553,221
Notice both answers equal 521,553,221

With that explanation out of the way, let's continue. Next, we take the number 521,553,221 and divide it by 2:

521,553,221 ÷ 2 = 260,776,610.5

If the quotient is a whole number, then 2 and 260,776,610.5 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:

1 521,553,221
-1 -521,553,221

Now, we try dividing 521,553,221 by 3:

521,553,221 ÷ 3 = 173,851,073.6667

If the quotient is a whole number, then 3 and 173,851,073.6667 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:

1 521,553,221
-1 -521,553,221

Let's try dividing by 4:

521,553,221 ÷ 4 = 130,388,305.25

If the quotient is a whole number, then 4 and 130,388,305.25 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:

1 521,553,221
-1 521,553,221
Keep dividing by the next highest number until you cannot divide anymore.

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

1723371612598515,95787,553612,8712,013,7193,239,46114,096,03322,676,22774,507,603521,553,221
-1-7-23-37-161-259-851-5,957-87,553-612,871-2,013,719-3,239,461-14,096,033-22,676,227-74,507,603-521,553,221

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