Q: What are the factor combinations of the number 331,103,213?

 A:
Positive:   1 x 3311032137 x 4730045967 x 4941839469 x 705977673 x 4919811049 x 3156374711 x 702837343 x 45091
Negative: -1 x -331103213-7 x -47300459-67 x -4941839-469 x -705977-673 x -491981-1049 x -315637-4711 x -70283-7343 x -45091


How do I find the factor combinations of the number 331,103,213?

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 331,103,213, 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.

1 331,103,213
-1 -331,103,213

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 331,103,213.

Example:
1 x 331,103,213 = 331,103,213
and
-1 x -331,103,213 = 331,103,213
Notice both answers equal 331,103,213

With that explanation out of the way, let's continue. Next, we take the number 331,103,213 and divide it by 2:

331,103,213 ÷ 2 = 165,551,606.5

If the quotient is a whole number, then 2 and 165,551,606.5 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:

1 331,103,213
-1 -331,103,213

Now, we try dividing 331,103,213 by 3:

331,103,213 ÷ 3 = 110,367,737.6667

If the quotient is a whole number, then 3 and 110,367,737.6667 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:

1 331,103,213
-1 -331,103,213

Let's try dividing by 4:

331,103,213 ÷ 4 = 82,775,803.25

If the quotient is a whole number, then 4 and 82,775,803.25 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:

1 331,103,213
-1 331,103,213
Keep dividing by the next highest number until you cannot divide anymore.

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

17674696731,0494,7117,34345,09170,283315,637491,981705,9774,941,83947,300,459331,103,213
-1-7-67-469-673-1,049-4,711-7,343-45,091-70,283-315,637-491,981-705,977-4,941,839-47,300,459-331,103,213

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