Q: What are the factor combinations of the number 12,005,215?

 A:
Positive:   1 x 120052155 x 240104331 x 38726573 x 164455155 x 77453365 x 328911061 x 113152263 x 5305
Negative: -1 x -12005215-5 x -2401043-31 x -387265-73 x -164455-155 x -77453-365 x -32891-1061 x -11315-2263 x -5305


How do I find the factor combinations of the number 12,005,215?

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 12,005,215, 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 12,005,215
-1 -12,005,215

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 12,005,215.

Example:
1 x 12,005,215 = 12,005,215
and
-1 x -12,005,215 = 12,005,215
Notice both answers equal 12,005,215

With that explanation out of the way, let's continue. Next, we take the number 12,005,215 and divide it by 2:

12,005,215 ÷ 2 = 6,002,607.5

If the quotient is a whole number, then 2 and 6,002,607.5 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 12,005,215
-1 -12,005,215

Now, we try dividing 12,005,215 by 3:

12,005,215 ÷ 3 = 4,001,738.3333

If the quotient is a whole number, then 3 and 4,001,738.3333 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 12,005,215
-1 -12,005,215

Let's try dividing by 4:

12,005,215 ÷ 4 = 3,001,303.75

If the quotient is a whole number, then 4 and 3,001,303.75 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 12,005,215
-1 12,005,215
Keep dividing by the next highest number until you cannot divide anymore.

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

1531731553651,0612,2635,30511,31532,89177,453164,455387,2652,401,04312,005,215
-1-5-31-73-155-365-1,061-2,263-5,305-11,315-32,891-77,453-164,455-387,265-2,401,043-12,005,215

More Examples

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