Q: What are the factor combinations of the number 27,919,031?

 A:
Positive:   1 x 279190317 x 3988433
Negative: -1 x -27919031-7 x -3988433


How do I find the factor combinations of the number 27,919,031?

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 27,919,031, 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 27,919,031
-1 -27,919,031

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 27,919,031.

Example:
1 x 27,919,031 = 27,919,031
and
-1 x -27,919,031 = 27,919,031
Notice both answers equal 27,919,031

With that explanation out of the way, let's continue. Next, we take the number 27,919,031 and divide it by 2:

27,919,031 ÷ 2 = 13,959,515.5

If the quotient is a whole number, then 2 and 13,959,515.5 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 27,919,031
-1 -27,919,031

Now, we try dividing 27,919,031 by 3:

27,919,031 ÷ 3 = 9,306,343.6667

If the quotient is a whole number, then 3 and 9,306,343.6667 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 27,919,031
-1 -27,919,031

Let's try dividing by 4:

27,919,031 ÷ 4 = 6,979,757.75

If the quotient is a whole number, then 4 and 6,979,757.75 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 27,919,031
-1 27,919,031
Keep dividing by the next highest number until you cannot divide anymore.

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

173,988,43327,919,031
-1-7-3,988,433-27,919,031

More Examples

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