Q: What are the factor combinations of the number 321,403,205?

 A:
Positive:   1 x 3214032055 x 6428064161 x 526890579 x 4068395305 x 1053781395 x 8136794819 x 6669513339 x 24095
Negative: -1 x -321403205-5 x -64280641-61 x -5268905-79 x -4068395-305 x -1053781-395 x -813679-4819 x -66695-13339 x -24095


How do I find the factor combinations of the number 321,403,205?

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 321,403,205, 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.

1 321,403,205
-1 -321,403,205

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 321,403,205.

Example:
1 x 321,403,205 = 321,403,205
and
-1 x -321,403,205 = 321,403,205
Notice both answers equal 321,403,205

With that explanation out of the way, let's continue. Next, we take the number 321,403,205 and divide it by 2:

321,403,205 ÷ 2 = 160,701,602.5

If the quotient is a whole number, then 2 and 160,701,602.5 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:

1 321,403,205
-1 -321,403,205

Now, we try dividing 321,403,205 by 3:

321,403,205 ÷ 3 = 107,134,401.6667

If the quotient is a whole number, then 3 and 107,134,401.6667 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:

1 321,403,205
-1 -321,403,205

Let's try dividing by 4:

321,403,205 ÷ 4 = 80,350,801.25

If the quotient is a whole number, then 4 and 80,350,801.25 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:

1 321,403,205
-1 321,403,205
Keep dividing by the next highest number until you cannot divide anymore.

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

1561793053954,81913,33924,09566,695813,6791,053,7814,068,3955,268,90564,280,641321,403,205
-1-5-61-79-305-395-4,819-13,339-24,095-66,695-813,679-1,053,781-4,068,395-5,268,905-64,280,641-321,403,205

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