Q: What are the factor combinations of the number 321,321,209?

 A:
Positive:   1 x 32132120911 x 2921101937 x 8684357109 x 2947901407 x 7894871199 x 2679914033 x 796737243 x 44363
Negative: -1 x -321321209-11 x -29211019-37 x -8684357-109 x -2947901-407 x -789487-1199 x -267991-4033 x -79673-7243 x -44363


How do I find the factor combinations of the number 321,321,209?

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 321,321,209, 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.

1 321,321,209
-1 -321,321,209

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 321,321,209.

Example:
1 x 321,321,209 = 321,321,209
and
-1 x -321,321,209 = 321,321,209
Notice both answers equal 321,321,209

With that explanation out of the way, let's continue. Next, we take the number 321,321,209 and divide it by 2:

321,321,209 ÷ 2 = 160,660,604.5

If the quotient is a whole number, then 2 and 160,660,604.5 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:

1 321,321,209
-1 -321,321,209

Now, we try dividing 321,321,209 by 3:

321,321,209 ÷ 3 = 107,107,069.6667

If the quotient is a whole number, then 3 and 107,107,069.6667 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:

1 321,321,209
-1 -321,321,209

Let's try dividing by 4:

321,321,209 ÷ 4 = 80,330,302.25

If the quotient is a whole number, then 4 and 80,330,302.25 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:

1 321,321,209
-1 321,321,209
Keep dividing by the next highest number until you cannot divide anymore.

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

111371094071,1994,0337,24344,36379,673267,991789,4872,947,9018,684,35729,211,019321,321,209
-1-11-37-109-407-1,199-4,033-7,243-44,363-79,673-267,991-789,487-2,947,901-8,684,357-29,211,019-321,321,209

More Examples

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