Q: What are the factor combinations of the number 321,303,005?

 A:
Positive:   1 x 3213030055 x 6426060137 x 8683865185 x 1736773467 x 6880152335 x 1376033719 x 8639517279 x 18595
Negative: -1 x -321303005-5 x -64260601-37 x -8683865-185 x -1736773-467 x -688015-2335 x -137603-3719 x -86395-17279 x -18595


How do I find the factor combinations of the number 321,303,005?

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 321,303,005, 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.

1 321,303,005
-1 -321,303,005

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 321,303,005.

Example:
1 x 321,303,005 = 321,303,005
and
-1 x -321,303,005 = 321,303,005
Notice both answers equal 321,303,005

With that explanation out of the way, let's continue. Next, we take the number 321,303,005 and divide it by 2:

321,303,005 ÷ 2 = 160,651,502.5

If the quotient is a whole number, then 2 and 160,651,502.5 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:

1 321,303,005
-1 -321,303,005

Now, we try dividing 321,303,005 by 3:

321,303,005 ÷ 3 = 107,101,001.6667

If the quotient is a whole number, then 3 and 107,101,001.6667 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:

1 321,303,005
-1 -321,303,005

Let's try dividing by 4:

321,303,005 ÷ 4 = 80,325,751.25

If the quotient is a whole number, then 4 and 80,325,751.25 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:

1 321,303,005
-1 321,303,005
Keep dividing by the next highest number until you cannot divide anymore.

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

15371854672,3353,71917,27918,59586,395137,603688,0151,736,7738,683,86564,260,601321,303,005
-1-5-37-185-467-2,335-3,719-17,279-18,595-86,395-137,603-688,015-1,736,773-8,683,865-64,260,601-321,303,005

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