Q: What are the factor combinations of the number 12,001,205?

 A:
Positive:   1 x 120012055 x 240024189 x 134845149 x 80545181 x 66305445 x 26969745 x 16109905 x 13261
Negative: -1 x -12001205-5 x -2400241-89 x -134845-149 x -80545-181 x -66305-445 x -26969-745 x -16109-905 x -13261


How do I find the factor combinations of the number 12,001,205?

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 12,001,205, 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 12,001,205
-1 -12,001,205

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 12,001,205.

Example:
1 x 12,001,205 = 12,001,205
and
-1 x -12,001,205 = 12,001,205
Notice both answers equal 12,001,205

With that explanation out of the way, let's continue. Next, we take the number 12,001,205 and divide it by 2:

12,001,205 ÷ 2 = 6,000,602.5

If the quotient is a whole number, then 2 and 6,000,602.5 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 12,001,205
-1 -12,001,205

Now, we try dividing 12,001,205 by 3:

12,001,205 ÷ 3 = 4,000,401.6667

If the quotient is a whole number, then 3 and 4,000,401.6667 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 12,001,205
-1 -12,001,205

Let's try dividing by 4:

12,001,205 ÷ 4 = 3,000,301.25

If the quotient is a whole number, then 4 and 3,000,301.25 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 12,001,205
-1 12,001,205
Keep dividing by the next highest number until you cannot divide anymore.

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

158914918144574590513,26116,10926,96966,30580,545134,8452,400,24112,001,205
-1-5-89-149-181-445-745-905-13,261-16,109-26,969-66,305-80,545-134,845-2,400,241-12,001,205

More Examples

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