Q: What are the factor combinations of the number 31,505,135?

 A:
Positive:   1 x 315051355 x 630102719 x 165816595 x 331633541 x 58235613 x 513952705 x 116473065 x 10279
Negative: -1 x -31505135-5 x -6301027-19 x -1658165-95 x -331633-541 x -58235-613 x -51395-2705 x -11647-3065 x -10279


How do I find the factor combinations of the number 31,505,135?

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 31,505,135, 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 31,505,135
-1 -31,505,135

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 31,505,135.

Example:
1 x 31,505,135 = 31,505,135
and
-1 x -31,505,135 = 31,505,135
Notice both answers equal 31,505,135

With that explanation out of the way, let's continue. Next, we take the number 31,505,135 and divide it by 2:

31,505,135 ÷ 2 = 15,752,567.5

If the quotient is a whole number, then 2 and 15,752,567.5 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 31,505,135
-1 -31,505,135

Now, we try dividing 31,505,135 by 3:

31,505,135 ÷ 3 = 10,501,711.6667

If the quotient is a whole number, then 3 and 10,501,711.6667 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 31,505,135
-1 -31,505,135

Let's try dividing by 4:

31,505,135 ÷ 4 = 7,876,283.75

If the quotient is a whole number, then 4 and 7,876,283.75 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 31,505,135
-1 31,505,135
Keep dividing by the next highest number until you cannot divide anymore.

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

1519955416132,7053,06510,27911,64751,39558,235331,6331,658,1656,301,02731,505,135
-1-5-19-95-541-613-2,705-3,065-10,279-11,647-51,395-58,235-331,633-1,658,165-6,301,027-31,505,135

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