Q: What are the factor combinations of the number 12,222,301?

 A:
Positive:   1 x 122223017 x 174604313 x 94017719 x 64327991 x 134311133 x 91897247 x 494831729 x 7069
Negative: -1 x -12222301-7 x -1746043-13 x -940177-19 x -643279-91 x -134311-133 x -91897-247 x -49483-1729 x -7069


How do I find the factor combinations of the number 12,222,301?

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 12,222,301, 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 12,222,301
-1 -12,222,301

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 12,222,301.

Example:
1 x 12,222,301 = 12,222,301
and
-1 x -12,222,301 = 12,222,301
Notice both answers equal 12,222,301

With that explanation out of the way, let's continue. Next, we take the number 12,222,301 and divide it by 2:

12,222,301 ÷ 2 = 6,111,150.5

If the quotient is a whole number, then 2 and 6,111,150.5 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 12,222,301
-1 -12,222,301

Now, we try dividing 12,222,301 by 3:

12,222,301 ÷ 3 = 4,074,100.3333

If the quotient is a whole number, then 3 and 4,074,100.3333 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 12,222,301
-1 -12,222,301

Let's try dividing by 4:

12,222,301 ÷ 4 = 3,055,575.25

If the quotient is a whole number, then 4 and 3,055,575.25 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 12,222,301
-1 12,222,301
Keep dividing by the next highest number until you cannot divide anymore.

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

171319911332471,7297,06949,48391,897134,311643,279940,1771,746,04312,222,301
-1-7-13-19-91-133-247-1,729-7,069-49,483-91,897-134,311-643,279-940,177-1,746,043-12,222,301

More Examples

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