Q: What are the factor combinations of the number 315,304,331?

 A:
Positive:   1 x 3153043317457 x 42283
Negative: -1 x -315304331-7457 x -42283


How do I find the factor combinations of the number 315,304,331?

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 315,304,331, 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.

1 315,304,331
-1 -315,304,331

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 315,304,331.

Example:
1 x 315,304,331 = 315,304,331
and
-1 x -315,304,331 = 315,304,331
Notice both answers equal 315,304,331

With that explanation out of the way, let's continue. Next, we take the number 315,304,331 and divide it by 2:

315,304,331 ÷ 2 = 157,652,165.5

If the quotient is a whole number, then 2 and 157,652,165.5 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:

1 315,304,331
-1 -315,304,331

Now, we try dividing 315,304,331 by 3:

315,304,331 ÷ 3 = 105,101,443.6667

If the quotient is a whole number, then 3 and 105,101,443.6667 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:

1 315,304,331
-1 -315,304,331

Let's try dividing by 4:

315,304,331 ÷ 4 = 78,826,082.75

If the quotient is a whole number, then 4 and 78,826,082.75 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:

1 315,304,331
-1 315,304,331
Keep dividing by the next highest number until you cannot divide anymore.

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

17,45742,283315,304,331
-1-7,457-42,283-315,304,331

More Examples

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