Q: What are the factor combinations of the number 31,215,119?

 A:
Positive:   1 x 3121511913 x 240116319 x 164290143 x 725933247 x 126377559 x 55841817 x 382072939 x 10621
Negative: -1 x -31215119-13 x -2401163-19 x -1642901-43 x -725933-247 x -126377-559 x -55841-817 x -38207-2939 x -10621


How do I find the factor combinations of the number 31,215,119?

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 31,215,119, 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 31,215,119
-1 -31,215,119

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 31,215,119.

Example:
1 x 31,215,119 = 31,215,119
and
-1 x -31,215,119 = 31,215,119
Notice both answers equal 31,215,119

With that explanation out of the way, let's continue. Next, we take the number 31,215,119 and divide it by 2:

31,215,119 ÷ 2 = 15,607,559.5

If the quotient is a whole number, then 2 and 15,607,559.5 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 31,215,119
-1 -31,215,119

Now, we try dividing 31,215,119 by 3:

31,215,119 ÷ 3 = 10,405,039.6667

If the quotient is a whole number, then 3 and 10,405,039.6667 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 31,215,119
-1 -31,215,119

Let's try dividing by 4:

31,215,119 ÷ 4 = 7,803,779.75

If the quotient is a whole number, then 4 and 7,803,779.75 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 31,215,119
-1 31,215,119
Keep dividing by the next highest number until you cannot divide anymore.

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

11319432475598172,93910,62138,20755,841126,377725,9331,642,9012,401,16331,215,119
-1-13-19-43-247-559-817-2,939-10,621-38,207-55,841-126,377-725,933-1,642,901-2,401,163-31,215,119

More Examples

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