Q: What are the factor combinations of the number 321,102,013?

 A:
Positive:   1 x 32110201359 x 5442407163 x 1969951173 x 1856081193 x 16637419617 x 3338910207 x 3145911387 x 28199
Negative: -1 x -321102013-59 x -5442407-163 x -1969951-173 x -1856081-193 x -1663741-9617 x -33389-10207 x -31459-11387 x -28199


How do I find the factor combinations of the number 321,102,013?

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 321,102,013, 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.

1 321,102,013
-1 -321,102,013

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 321,102,013.

Example:
1 x 321,102,013 = 321,102,013
and
-1 x -321,102,013 = 321,102,013
Notice both answers equal 321,102,013

With that explanation out of the way, let's continue. Next, we take the number 321,102,013 and divide it by 2:

321,102,013 ÷ 2 = 160,551,006.5

If the quotient is a whole number, then 2 and 160,551,006.5 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:

1 321,102,013
-1 -321,102,013

Now, we try dividing 321,102,013 by 3:

321,102,013 ÷ 3 = 107,034,004.3333

If the quotient is a whole number, then 3 and 107,034,004.3333 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:

1 321,102,013
-1 -321,102,013

Let's try dividing by 4:

321,102,013 ÷ 4 = 80,275,503.25

If the quotient is a whole number, then 4 and 80,275,503.25 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:

1 321,102,013
-1 321,102,013
Keep dividing by the next highest number until you cannot divide anymore.

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

1591631731939,61710,20711,38728,19931,45933,3891,663,7411,856,0811,969,9515,442,407321,102,013
-1-59-163-173-193-9,617-10,207-11,387-28,199-31,459-33,389-1,663,741-1,856,081-1,969,951-5,442,407-321,102,013

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