Q: What are the factor combinations of the number 321,021,235?

 A:
Positive:   1 x 3210212355 x 6420424723 x 13957445115 x 2791489787 x 4079053547 x 905053935 x 8158117735 x 18101
Negative: -1 x -321021235-5 x -64204247-23 x -13957445-115 x -2791489-787 x -407905-3547 x -90505-3935 x -81581-17735 x -18101


How do I find the factor combinations of the number 321,021,235?

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 321,021,235, 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.

1 321,021,235
-1 -321,021,235

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 321,021,235.

Example:
1 x 321,021,235 = 321,021,235
and
-1 x -321,021,235 = 321,021,235
Notice both answers equal 321,021,235

With that explanation out of the way, let's continue. Next, we take the number 321,021,235 and divide it by 2:

321,021,235 ÷ 2 = 160,510,617.5

If the quotient is a whole number, then 2 and 160,510,617.5 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:

1 321,021,235
-1 -321,021,235

Now, we try dividing 321,021,235 by 3:

321,021,235 ÷ 3 = 107,007,078.3333

If the quotient is a whole number, then 3 and 107,007,078.3333 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:

1 321,021,235
-1 -321,021,235

Let's try dividing by 4:

321,021,235 ÷ 4 = 80,255,308.75

If the quotient is a whole number, then 4 and 80,255,308.75 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:

1 321,021,235
-1 321,021,235
Keep dividing by the next highest number until you cannot divide anymore.

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

15231157873,5473,93517,73518,10181,58190,505407,9052,791,48913,957,44564,204,247321,021,235
-1-5-23-115-787-3,547-3,935-17,735-18,101-81,581-90,505-407,905-2,791,489-13,957,445-64,204,247-321,021,235

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