Q: What are the factor combinations of the number 13,331,213?

 A:
Positive:   1 x 133312137 x 190445917 x 78418929 x 459697119 x 112027203 x 65671493 x 270413451 x 3863
Negative: -1 x -13331213-7 x -1904459-17 x -784189-29 x -459697-119 x -112027-203 x -65671-493 x -27041-3451 x -3863


How do I find the factor combinations of the number 13,331,213?

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 13,331,213, 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 13,331,213
-1 -13,331,213

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 13,331,213.

Example:
1 x 13,331,213 = 13,331,213
and
-1 x -13,331,213 = 13,331,213
Notice both answers equal 13,331,213

With that explanation out of the way, let's continue. Next, we take the number 13,331,213 and divide it by 2:

13,331,213 ÷ 2 = 6,665,606.5

If the quotient is a whole number, then 2 and 6,665,606.5 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 13,331,213
-1 -13,331,213

Now, we try dividing 13,331,213 by 3:

13,331,213 ÷ 3 = 4,443,737.6667

If the quotient is a whole number, then 3 and 4,443,737.6667 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 13,331,213
-1 -13,331,213

Let's try dividing by 4:

13,331,213 ÷ 4 = 3,332,803.25

If the quotient is a whole number, then 4 and 3,332,803.25 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 13,331,213
-1 13,331,213
Keep dividing by the next highest number until you cannot divide anymore.

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

1717291192034933,4513,86327,04165,671112,027459,697784,1891,904,45913,331,213
-1-7-17-29-119-203-493-3,451-3,863-27,041-65,671-112,027-459,697-784,189-1,904,459-13,331,213

More Examples

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