Q: What are the factor combinations of the number 321,133,309?

 A:
Positive:   1 x 3211333097 x 4587618731 x 1035913949 x 6553741163 x 1970143217 x 14798771141 x 2814491297 x 2475971519 x 2114115053 x 635537987 x 402079079 x 35371
Negative: -1 x -321133309-7 x -45876187-31 x -10359139-49 x -6553741-163 x -1970143-217 x -1479877-1141 x -281449-1297 x -247597-1519 x -211411-5053 x -63553-7987 x -40207-9079 x -35371


How do I find the factor combinations of the number 321,133,309?

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 321,133,309, 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.

1 321,133,309
-1 -321,133,309

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 321,133,309.

Example:
1 x 321,133,309 = 321,133,309
and
-1 x -321,133,309 = 321,133,309
Notice both answers equal 321,133,309

With that explanation out of the way, let's continue. Next, we take the number 321,133,309 and divide it by 2:

321,133,309 ÷ 2 = 160,566,654.5

If the quotient is a whole number, then 2 and 160,566,654.5 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:

1 321,133,309
-1 -321,133,309

Now, we try dividing 321,133,309 by 3:

321,133,309 ÷ 3 = 107,044,436.3333

If the quotient is a whole number, then 3 and 107,044,436.3333 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:

1 321,133,309
-1 -321,133,309

Let's try dividing by 4:

321,133,309 ÷ 4 = 80,283,327.25

If the quotient is a whole number, then 4 and 80,283,327.25 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:

1 321,133,309
-1 321,133,309
Keep dividing by the next highest number until you cannot divide anymore.

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

1731491632171,1411,2971,5195,0537,9879,07935,37140,20763,553211,411247,597281,4491,479,8771,970,1436,553,74110,359,13945,876,187321,133,309
-1-7-31-49-163-217-1,141-1,297-1,519-5,053-7,987-9,079-35,371-40,207-63,553-211,411-247,597-281,449-1,479,877-1,970,143-6,553,741-10,359,139-45,876,187-321,133,309

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