Q: What are the factor combinations of the number 331,102,409?

 A:
Positive:   1 x 33110240911 x 3010021967 x 4941827523 x 633083737 x 449257859 x 3854515753 x 575539449 x 35041
Negative: -1 x -331102409-11 x -30100219-67 x -4941827-523 x -633083-737 x -449257-859 x -385451-5753 x -57553-9449 x -35041


How do I find the factor combinations of the number 331,102,409?

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 331,102,409, 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.

1 331,102,409
-1 -331,102,409

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 331,102,409.

Example:
1 x 331,102,409 = 331,102,409
and
-1 x -331,102,409 = 331,102,409
Notice both answers equal 331,102,409

With that explanation out of the way, let's continue. Next, we take the number 331,102,409 and divide it by 2:

331,102,409 ÷ 2 = 165,551,204.5

If the quotient is a whole number, then 2 and 165,551,204.5 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:

1 331,102,409
-1 -331,102,409

Now, we try dividing 331,102,409 by 3:

331,102,409 ÷ 3 = 110,367,469.6667

If the quotient is a whole number, then 3 and 110,367,469.6667 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:

1 331,102,409
-1 -331,102,409

Let's try dividing by 4:

331,102,409 ÷ 4 = 82,775,602.25

If the quotient is a whole number, then 4 and 82,775,602.25 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:

1 331,102,409
-1 331,102,409
Keep dividing by the next highest number until you cannot divide anymore.

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

111675237378595,7539,44935,04157,553385,451449,257633,0834,941,82730,100,219331,102,409
-1-11-67-523-737-859-5,753-9,449-35,041-57,553-385,451-449,257-633,083-4,941,827-30,100,219-331,102,409

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