Q: What are the factor combinations of the number 31,348,603?

 A:
Positive:   1 x 3134860311 x 284987313 x 2411431143 x 219221257 x 121979853 x 367512827 x 110893341 x 9383
Negative: -1 x -31348603-11 x -2849873-13 x -2411431-143 x -219221-257 x -121979-853 x -36751-2827 x -11089-3341 x -9383


How do I find the factor combinations of the number 31,348,603?

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 31,348,603, 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 31,348,603
-1 -31,348,603

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 31,348,603.

Example:
1 x 31,348,603 = 31,348,603
and
-1 x -31,348,603 = 31,348,603
Notice both answers equal 31,348,603

With that explanation out of the way, let's continue. Next, we take the number 31,348,603 and divide it by 2:

31,348,603 ÷ 2 = 15,674,301.5

If the quotient is a whole number, then 2 and 15,674,301.5 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 31,348,603
-1 -31,348,603

Now, we try dividing 31,348,603 by 3:

31,348,603 ÷ 3 = 10,449,534.3333

If the quotient is a whole number, then 3 and 10,449,534.3333 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 31,348,603
-1 -31,348,603

Let's try dividing by 4:

31,348,603 ÷ 4 = 7,837,150.75

If the quotient is a whole number, then 4 and 7,837,150.75 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 31,348,603
-1 31,348,603
Keep dividing by the next highest number until you cannot divide anymore.

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

111131432578532,8273,3419,38311,08936,751121,979219,2212,411,4312,849,87331,348,603
-1-11-13-143-257-853-2,827-3,341-9,383-11,089-36,751-121,979-219,221-2,411,431-2,849,873-31,348,603

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