Q: What are the factor combinations of the number 321,223,313?

 A:
Positive:   1 x 32122331317 x 1889548923 x 13966231391 x 821543811 x 3960831013 x 31710113787 x 2329917221 x 18653
Negative: -1 x -321223313-17 x -18895489-23 x -13966231-391 x -821543-811 x -396083-1013 x -317101-13787 x -23299-17221 x -18653


How do I find the factor combinations of the number 321,223,313?

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 321,223,313, 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.

1 321,223,313
-1 -321,223,313

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 321,223,313.

Example:
1 x 321,223,313 = 321,223,313
and
-1 x -321,223,313 = 321,223,313
Notice both answers equal 321,223,313

With that explanation out of the way, let's continue. Next, we take the number 321,223,313 and divide it by 2:

321,223,313 ÷ 2 = 160,611,656.5

If the quotient is a whole number, then 2 and 160,611,656.5 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:

1 321,223,313
-1 -321,223,313

Now, we try dividing 321,223,313 by 3:

321,223,313 ÷ 3 = 107,074,437.6667

If the quotient is a whole number, then 3 and 107,074,437.6667 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:

1 321,223,313
-1 -321,223,313

Let's try dividing by 4:

321,223,313 ÷ 4 = 80,305,828.25

If the quotient is a whole number, then 4 and 80,305,828.25 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:

1 321,223,313
-1 321,223,313
Keep dividing by the next highest number until you cannot divide anymore.

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

117233918111,01313,78717,22118,65323,299317,101396,083821,54313,966,23118,895,489321,223,313
-1-17-23-391-811-1,013-13,787-17,221-18,653-23,299-317,101-396,083-821,543-13,966,231-18,895,489-321,223,313

More Examples

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