Q: What are the factor combinations of the number 321,042,305?

 A:
Positive:   1 x 3210423055 x 6420846159 x 5441395295 x 1088279563 x 5702351933 x 1660852815 x 1140479665 x 33217
Negative: -1 x -321042305-5 x -64208461-59 x -5441395-295 x -1088279-563 x -570235-1933 x -166085-2815 x -114047-9665 x -33217


How do I find the factor combinations of the number 321,042,305?

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 321,042,305, 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.

1 321,042,305
-1 -321,042,305

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 321,042,305.

Example:
1 x 321,042,305 = 321,042,305
and
-1 x -321,042,305 = 321,042,305
Notice both answers equal 321,042,305

With that explanation out of the way, let's continue. Next, we take the number 321,042,305 and divide it by 2:

321,042,305 ÷ 2 = 160,521,152.5

If the quotient is a whole number, then 2 and 160,521,152.5 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:

1 321,042,305
-1 -321,042,305

Now, we try dividing 321,042,305 by 3:

321,042,305 ÷ 3 = 107,014,101.6667

If the quotient is a whole number, then 3 and 107,014,101.6667 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:

1 321,042,305
-1 -321,042,305

Let's try dividing by 4:

321,042,305 ÷ 4 = 80,260,576.25

If the quotient is a whole number, then 4 and 80,260,576.25 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:

1 321,042,305
-1 321,042,305
Keep dividing by the next highest number until you cannot divide anymore.

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

15592955631,9332,8159,66533,217114,047166,085570,2351,088,2795,441,39564,208,461321,042,305
-1-5-59-295-563-1,933-2,815-9,665-33,217-114,047-166,085-570,235-1,088,279-5,441,395-64,208,461-321,042,305

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