Q: What are the factor combinations of the number 310,246,517?

 A:
Positive:   1 x 3102465177 x 4432093123 x 1348897937 x 8385041161 x 1926997259 x 1197863851 x 3645675957 x 52081
Negative: -1 x -310246517-7 x -44320931-23 x -13488979-37 x -8385041-161 x -1926997-259 x -1197863-851 x -364567-5957 x -52081


How do I find the factor combinations of the number 310,246,517?

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 310,246,517, 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.

1 310,246,517
-1 -310,246,517

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 310,246,517.

Example:
1 x 310,246,517 = 310,246,517
and
-1 x -310,246,517 = 310,246,517
Notice both answers equal 310,246,517

With that explanation out of the way, let's continue. Next, we take the number 310,246,517 and divide it by 2:

310,246,517 ÷ 2 = 155,123,258.5

If the quotient is a whole number, then 2 and 155,123,258.5 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:

1 310,246,517
-1 -310,246,517

Now, we try dividing 310,246,517 by 3:

310,246,517 ÷ 3 = 103,415,505.6667

If the quotient is a whole number, then 3 and 103,415,505.6667 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:

1 310,246,517
-1 -310,246,517

Let's try dividing by 4:

310,246,517 ÷ 4 = 77,561,629.25

If the quotient is a whole number, then 4 and 77,561,629.25 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:

1 310,246,517
-1 310,246,517
Keep dividing by the next highest number until you cannot divide anymore.

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

1723371612598515,95752,081364,5671,197,8631,926,9978,385,04113,488,97944,320,931310,246,517
-1-7-23-37-161-259-851-5,957-52,081-364,567-1,197,863-1,926,997-8,385,041-13,488,979-44,320,931-310,246,517

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