Q: What are the factor combinations of the number 311,125,405?

 A:
Positive:   1 x 3111254055 x 62225081103 x 3020635347 x 896615515 x 6041271735 x 1793231741 x 1787058705 x 35741
Negative: -1 x -311125405-5 x -62225081-103 x -3020635-347 x -896615-515 x -604127-1735 x -179323-1741 x -178705-8705 x -35741


How do I find the factor combinations of the number 311,125,405?

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 311,125,405, 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.

1 311,125,405
-1 -311,125,405

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 311,125,405.

Example:
1 x 311,125,405 = 311,125,405
and
-1 x -311,125,405 = 311,125,405
Notice both answers equal 311,125,405

With that explanation out of the way, let's continue. Next, we take the number 311,125,405 and divide it by 2:

311,125,405 ÷ 2 = 155,562,702.5

If the quotient is a whole number, then 2 and 155,562,702.5 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:

1 311,125,405
-1 -311,125,405

Now, we try dividing 311,125,405 by 3:

311,125,405 ÷ 3 = 103,708,468.3333

If the quotient is a whole number, then 3 and 103,708,468.3333 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:

1 311,125,405
-1 -311,125,405

Let's try dividing by 4:

311,125,405 ÷ 4 = 77,781,351.25

If the quotient is a whole number, then 4 and 77,781,351.25 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:

1 311,125,405
-1 311,125,405
Keep dividing by the next highest number until you cannot divide anymore.

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

151033475151,7351,7418,70535,741178,705179,323604,127896,6153,020,63562,225,081311,125,405
-1-5-103-347-515-1,735-1,741-8,705-35,741-178,705-179,323-604,127-896,615-3,020,635-62,225,081-311,125,405

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