Q: What are the factor combinations of the number 12,010,105?

 A:
Positive:   1 x 120101055 x 240202189 x 134945137 x 87665197 x 60965445 x 26989685 x 17533985 x 12193
Negative: -1 x -12010105-5 x -2402021-89 x -134945-137 x -87665-197 x -60965-445 x -26989-685 x -17533-985 x -12193


How do I find the factor combinations of the number 12,010,105?

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 12,010,105, 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 12,010,105
-1 -12,010,105

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 12,010,105.

Example:
1 x 12,010,105 = 12,010,105
and
-1 x -12,010,105 = 12,010,105
Notice both answers equal 12,010,105

With that explanation out of the way, let's continue. Next, we take the number 12,010,105 and divide it by 2:

12,010,105 ÷ 2 = 6,005,052.5

If the quotient is a whole number, then 2 and 6,005,052.5 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 12,010,105
-1 -12,010,105

Now, we try dividing 12,010,105 by 3:

12,010,105 ÷ 3 = 4,003,368.3333

If the quotient is a whole number, then 3 and 4,003,368.3333 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 12,010,105
-1 -12,010,105

Let's try dividing by 4:

12,010,105 ÷ 4 = 3,002,526.25

If the quotient is a whole number, then 4 and 3,002,526.25 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 12,010,105
-1 12,010,105
Keep dividing by the next highest number until you cannot divide anymore.

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

158913719744568598512,19317,53326,98960,96587,665134,9452,402,02112,010,105
-1-5-89-137-197-445-685-985-12,193-17,533-26,989-60,965-87,665-134,945-2,402,021-12,010,105

More Examples

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