Q: What are the factor combinations of the number 321,313,345?

 A:
Positive:   1 x 3213133455 x 6426266917 x 1890078585 x 37801571789 x 1796052113 x 1520658945 x 3592110565 x 30413
Negative: -1 x -321313345-5 x -64262669-17 x -18900785-85 x -3780157-1789 x -179605-2113 x -152065-8945 x -35921-10565 x -30413


How do I find the factor combinations of the number 321,313,345?

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 321,313,345, 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.

1 321,313,345
-1 -321,313,345

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 321,313,345.

Example:
1 x 321,313,345 = 321,313,345
and
-1 x -321,313,345 = 321,313,345
Notice both answers equal 321,313,345

With that explanation out of the way, let's continue. Next, we take the number 321,313,345 and divide it by 2:

321,313,345 ÷ 2 = 160,656,672.5

If the quotient is a whole number, then 2 and 160,656,672.5 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:

1 321,313,345
-1 -321,313,345

Now, we try dividing 321,313,345 by 3:

321,313,345 ÷ 3 = 107,104,448.3333

If the quotient is a whole number, then 3 and 107,104,448.3333 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:

1 321,313,345
-1 -321,313,345

Let's try dividing by 4:

321,313,345 ÷ 4 = 80,328,336.25

If the quotient is a whole number, then 4 and 80,328,336.25 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:

1 321,313,345
-1 321,313,345
Keep dividing by the next highest number until you cannot divide anymore.

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

1517851,7892,1138,94510,56530,41335,921152,065179,6053,780,15718,900,78564,262,669321,313,345
-1-5-17-85-1,789-2,113-8,945-10,565-30,413-35,921-152,065-179,605-3,780,157-18,900,785-64,262,669-321,313,345

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