Q: What are the factor combinations of the number 31,524,233?

 A:
Positive:   1 x 3152423313 x 2424941107 x 294619131 x 240643173 x 1822211391 x 226631703 x 185112249 x 14017
Negative: -1 x -31524233-13 x -2424941-107 x -294619-131 x -240643-173 x -182221-1391 x -22663-1703 x -18511-2249 x -14017


How do I find the factor combinations of the number 31,524,233?

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 31,524,233, 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 31,524,233
-1 -31,524,233

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 31,524,233.

Example:
1 x 31,524,233 = 31,524,233
and
-1 x -31,524,233 = 31,524,233
Notice both answers equal 31,524,233

With that explanation out of the way, let's continue. Next, we take the number 31,524,233 and divide it by 2:

31,524,233 ÷ 2 = 15,762,116.5

If the quotient is a whole number, then 2 and 15,762,116.5 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 31,524,233
-1 -31,524,233

Now, we try dividing 31,524,233 by 3:

31,524,233 ÷ 3 = 10,508,077.6667

If the quotient is a whole number, then 3 and 10,508,077.6667 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 31,524,233
-1 -31,524,233

Let's try dividing by 4:

31,524,233 ÷ 4 = 7,881,058.25

If the quotient is a whole number, then 4 and 7,881,058.25 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 31,524,233
-1 31,524,233
Keep dividing by the next highest number until you cannot divide anymore.

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

1131071311731,3911,7032,24914,01718,51122,663182,221240,643294,6192,424,94131,524,233
-1-13-107-131-173-1,391-1,703-2,249-14,017-18,511-22,663-182,221-240,643-294,619-2,424,941-31,524,233

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