Q: What are the factor combinations of the number 13,506,221?

 A:
Positive:   1 x 1350622123 x 58722737 x 36503359 x 228919269 x 50209851 x 158711357 x 99532183 x 6187
Negative: -1 x -13506221-23 x -587227-37 x -365033-59 x -228919-269 x -50209-851 x -15871-1357 x -9953-2183 x -6187


How do I find the factor combinations of the number 13,506,221?

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 13,506,221, 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 13,506,221
-1 -13,506,221

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 13,506,221.

Example:
1 x 13,506,221 = 13,506,221
and
-1 x -13,506,221 = 13,506,221
Notice both answers equal 13,506,221

With that explanation out of the way, let's continue. Next, we take the number 13,506,221 and divide it by 2:

13,506,221 ÷ 2 = 6,753,110.5

If the quotient is a whole number, then 2 and 6,753,110.5 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 13,506,221
-1 -13,506,221

Now, we try dividing 13,506,221 by 3:

13,506,221 ÷ 3 = 4,502,073.6667

If the quotient is a whole number, then 3 and 4,502,073.6667 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 13,506,221
-1 -13,506,221

Let's try dividing by 4:

13,506,221 ÷ 4 = 3,376,555.25

If the quotient is a whole number, then 4 and 3,376,555.25 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 13,506,221
-1 13,506,221
Keep dividing by the next highest number until you cannot divide anymore.

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

12337592698511,3572,1836,1879,95315,87150,209228,919365,033587,22713,506,221
-1-23-37-59-269-851-1,357-2,183-6,187-9,953-15,871-50,209-228,919-365,033-587,227-13,506,221

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