Q: What are the factor combinations of the number 315,071,105?

 A:
Positive:   1 x 3150711055 x 6301422143 x 7327235215 x 1465447409 x 7703452045 x 1540693583 x 8793517587 x 17915
Negative: -1 x -315071105-5 x -63014221-43 x -7327235-215 x -1465447-409 x -770345-2045 x -154069-3583 x -87935-17587 x -17915


How do I find the factor combinations of the number 315,071,105?

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 315,071,105, 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.

1 315,071,105
-1 -315,071,105

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 315,071,105.

Example:
1 x 315,071,105 = 315,071,105
and
-1 x -315,071,105 = 315,071,105
Notice both answers equal 315,071,105

With that explanation out of the way, let's continue. Next, we take the number 315,071,105 and divide it by 2:

315,071,105 ÷ 2 = 157,535,552.5

If the quotient is a whole number, then 2 and 157,535,552.5 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:

1 315,071,105
-1 -315,071,105

Now, we try dividing 315,071,105 by 3:

315,071,105 ÷ 3 = 105,023,701.6667

If the quotient is a whole number, then 3 and 105,023,701.6667 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:

1 315,071,105
-1 -315,071,105

Let's try dividing by 4:

315,071,105 ÷ 4 = 78,767,776.25

If the quotient is a whole number, then 4 and 78,767,776.25 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:

1 315,071,105
-1 315,071,105
Keep dividing by the next highest number until you cannot divide anymore.

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

15432154092,0453,58317,58717,91587,935154,069770,3451,465,4477,327,23563,014,221315,071,105
-1-5-43-215-409-2,045-3,583-17,587-17,915-87,935-154,069-770,345-1,465,447-7,327,235-63,014,221-315,071,105

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