Q: What are the factor combinations of the number 321,231,133?

 A:
Positive:   1 x 32123113317 x 1889594923 x 13966571127 x 2529379391 x 8215632159 x 1487872921 x 1099736469 x 49657
Negative: -1 x -321231133-17 x -18895949-23 x -13966571-127 x -2529379-391 x -821563-2159 x -148787-2921 x -109973-6469 x -49657


How do I find the factor combinations of the number 321,231,133?

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 321,231,133, 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.

1 321,231,133
-1 -321,231,133

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 321,231,133.

Example:
1 x 321,231,133 = 321,231,133
and
-1 x -321,231,133 = 321,231,133
Notice both answers equal 321,231,133

With that explanation out of the way, let's continue. Next, we take the number 321,231,133 and divide it by 2:

321,231,133 ÷ 2 = 160,615,566.5

If the quotient is a whole number, then 2 and 160,615,566.5 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:

1 321,231,133
-1 -321,231,133

Now, we try dividing 321,231,133 by 3:

321,231,133 ÷ 3 = 107,077,044.3333

If the quotient is a whole number, then 3 and 107,077,044.3333 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:

1 321,231,133
-1 -321,231,133

Let's try dividing by 4:

321,231,133 ÷ 4 = 80,307,783.25

If the quotient is a whole number, then 4 and 80,307,783.25 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:

1 321,231,133
-1 321,231,133
Keep dividing by the next highest number until you cannot divide anymore.

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

117231273912,1592,9216,46949,657109,973148,787821,5632,529,37913,966,57118,895,949321,231,133
-1-17-23-127-391-2,159-2,921-6,469-49,657-109,973-148,787-821,563-2,529,379-13,966,571-18,895,949-321,231,133

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