Q: What are the factor combinations of the number 31,303,405?

 A:
Positive:   1 x 313034055 x 62606817 x 447191535 x 89438349 x 63884567 x 467215245 x 127769335 x 93443469 x 667451907 x 164152345 x 133493283 x 9535
Negative: -1 x -31303405-5 x -6260681-7 x -4471915-35 x -894383-49 x -638845-67 x -467215-245 x -127769-335 x -93443-469 x -66745-1907 x -16415-2345 x -13349-3283 x -9535


How do I find the factor combinations of the number 31,303,405?

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 31,303,405, 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 31,303,405
-1 -31,303,405

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 31,303,405.

Example:
1 x 31,303,405 = 31,303,405
and
-1 x -31,303,405 = 31,303,405
Notice both answers equal 31,303,405

With that explanation out of the way, let's continue. Next, we take the number 31,303,405 and divide it by 2:

31,303,405 ÷ 2 = 15,651,702.5

If the quotient is a whole number, then 2 and 15,651,702.5 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 31,303,405
-1 -31,303,405

Now, we try dividing 31,303,405 by 3:

31,303,405 ÷ 3 = 10,434,468.3333

If the quotient is a whole number, then 3 and 10,434,468.3333 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 31,303,405
-1 -31,303,405

Let's try dividing by 4:

31,303,405 ÷ 4 = 7,825,851.25

If the quotient is a whole number, then 4 and 7,825,851.25 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 31,303,405
-1 31,303,405
Keep dividing by the next highest number until you cannot divide anymore.

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

1573549672453354691,9072,3453,2839,53513,34916,41566,74593,443127,769467,215638,845894,3834,471,9156,260,68131,303,405
-1-5-7-35-49-67-245-335-469-1,907-2,345-3,283-9,535-13,349-16,415-66,745-93,443-127,769-467,215-638,845-894,383-4,471,915-6,260,681-31,303,405

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