Q: What are the factor combinations of the number 31,300,643?

 A:
Positive:   1 x 3130064311 x 2845513121 x 258683167 x 1874291549 x 202071837 x 17039
Negative: -1 x -31300643-11 x -2845513-121 x -258683-167 x -187429-1549 x -20207-1837 x -17039


How do I find the factor combinations of the number 31,300,643?

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 31,300,643, 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 31,300,643
-1 -31,300,643

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 31,300,643.

Example:
1 x 31,300,643 = 31,300,643
and
-1 x -31,300,643 = 31,300,643
Notice both answers equal 31,300,643

With that explanation out of the way, let's continue. Next, we take the number 31,300,643 and divide it by 2:

31,300,643 ÷ 2 = 15,650,321.5

If the quotient is a whole number, then 2 and 15,650,321.5 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 31,300,643
-1 -31,300,643

Now, we try dividing 31,300,643 by 3:

31,300,643 ÷ 3 = 10,433,547.6667

If the quotient is a whole number, then 3 and 10,433,547.6667 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 31,300,643
-1 -31,300,643

Let's try dividing by 4:

31,300,643 ÷ 4 = 7,825,160.75

If the quotient is a whole number, then 4 and 7,825,160.75 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 31,300,643
-1 31,300,643
Keep dividing by the next highest number until you cannot divide anymore.

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

1111211671,5491,83717,03920,207187,429258,6832,845,51331,300,643
-1-11-121-167-1,549-1,837-17,039-20,207-187,429-258,683-2,845,513-31,300,643

More Examples

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