Q: What are the factor combinations of the number 12,005?

 A:
Positive:   1 x 120055 x 24017 x 171535 x 34349 x 245
Negative: -1 x -12005-5 x -2401-7 x -1715-35 x -343-49 x -245


How do I find the factor combinations of the number 12,005?

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 12,005, 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 12,005
-1 -12,005

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 12,005.

Example:
1 x 12,005 = 12,005
and
-1 x -12,005 = 12,005
Notice both answers equal 12,005

With that explanation out of the way, let's continue. Next, we take the number 12,005 and divide it by 2:

12,005 ÷ 2 = 6,002.5

If the quotient is a whole number, then 2 and 6,002.5 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 12,005
-1 -12,005

Now, we try dividing 12,005 by 3:

12,005 ÷ 3 = 4,001.6667

If the quotient is a whole number, then 3 and 4,001.6667 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 12,005
-1 -12,005

Let's try dividing by 4:

12,005 ÷ 4 = 3,001.25

If the quotient is a whole number, then 4 and 3,001.25 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 12,005
-1 12,005
Keep dividing by the next highest number until you cannot divide anymore.

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

15735492453431,7152,40112,005
-1-5-7-35-49-245-343-1,715-2,401-12,005

More Examples

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