Q: What are the factor combinations of the number 27,215,021?

 A:
Positive:   1 x 2721502129 x 93844941 x 66378147 x 579043487 x 558831189 x 228891363 x 199671927 x 14123
Negative: -1 x -27215021-29 x -938449-41 x -663781-47 x -579043-487 x -55883-1189 x -22889-1363 x -19967-1927 x -14123


How do I find the factor combinations of the number 27,215,021?

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 27,215,021, 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 27,215,021
-1 -27,215,021

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 27,215,021.

Example:
1 x 27,215,021 = 27,215,021
and
-1 x -27,215,021 = 27,215,021
Notice both answers equal 27,215,021

With that explanation out of the way, let's continue. Next, we take the number 27,215,021 and divide it by 2:

27,215,021 ÷ 2 = 13,607,510.5

If the quotient is a whole number, then 2 and 13,607,510.5 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 27,215,021
-1 -27,215,021

Now, we try dividing 27,215,021 by 3:

27,215,021 ÷ 3 = 9,071,673.6667

If the quotient is a whole number, then 3 and 9,071,673.6667 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 27,215,021
-1 -27,215,021

Let's try dividing by 4:

27,215,021 ÷ 4 = 6,803,755.25

If the quotient is a whole number, then 4 and 6,803,755.25 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 27,215,021
-1 27,215,021
Keep dividing by the next highest number until you cannot divide anymore.

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

12941474871,1891,3631,92714,12319,96722,88955,883579,043663,781938,44927,215,021
-1-29-41-47-487-1,189-1,363-1,927-14,123-19,967-22,889-55,883-579,043-663,781-938,449-27,215,021

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