Q: What are the factor combinations of the number 12,222,223?

 A:
Positive:   1 x 1222222313 x 94017123 x 53140141 x 298103299 x 40877533 x 22931943 x 12961997 x 12259
Negative: -1 x -12222223-13 x -940171-23 x -531401-41 x -298103-299 x -40877-533 x -22931-943 x -12961-997 x -12259


How do I find the factor combinations of the number 12,222,223?

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 12,222,223, 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 12,222,223
-1 -12,222,223

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 12,222,223.

Example:
1 x 12,222,223 = 12,222,223
and
-1 x -12,222,223 = 12,222,223
Notice both answers equal 12,222,223

With that explanation out of the way, let's continue. Next, we take the number 12,222,223 and divide it by 2:

12,222,223 ÷ 2 = 6,111,111.5

If the quotient is a whole number, then 2 and 6,111,111.5 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 12,222,223
-1 -12,222,223

Now, we try dividing 12,222,223 by 3:

12,222,223 ÷ 3 = 4,074,074.3333

If the quotient is a whole number, then 3 and 4,074,074.3333 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 12,222,223
-1 -12,222,223

Let's try dividing by 4:

12,222,223 ÷ 4 = 3,055,555.75

If the quotient is a whole number, then 4 and 3,055,555.75 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 12,222,223
-1 12,222,223
Keep dividing by the next highest number until you cannot divide anymore.

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

113234129953394399712,25912,96122,93140,877298,103531,401940,17112,222,223
-1-13-23-41-299-533-943-997-12,259-12,961-22,931-40,877-298,103-531,401-940,171-12,222,223

More Examples

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