Q: What are the factor combinations of the number 31,132,123?

 A:
Positive:   1 x 3113212311 x 2830193151 x 2061731661 x 18743
Negative: -1 x -31132123-11 x -2830193-151 x -206173-1661 x -18743


How do I find the factor combinations of the number 31,132,123?

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 31,132,123, 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 31,132,123
-1 -31,132,123

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 31,132,123.

Example:
1 x 31,132,123 = 31,132,123
and
-1 x -31,132,123 = 31,132,123
Notice both answers equal 31,132,123

With that explanation out of the way, let's continue. Next, we take the number 31,132,123 and divide it by 2:

31,132,123 ÷ 2 = 15,566,061.5

If the quotient is a whole number, then 2 and 15,566,061.5 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 31,132,123
-1 -31,132,123

Now, we try dividing 31,132,123 by 3:

31,132,123 ÷ 3 = 10,377,374.3333

If the quotient is a whole number, then 3 and 10,377,374.3333 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 31,132,123
-1 -31,132,123

Let's try dividing by 4:

31,132,123 ÷ 4 = 7,783,030.75

If the quotient is a whole number, then 4 and 7,783,030.75 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 31,132,123
-1 31,132,123
Keep dividing by the next highest number until you cannot divide anymore.

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

1111511,66118,743206,1732,830,19331,132,123
-1-11-151-1,661-18,743-206,173-2,830,193-31,132,123

More Examples

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