Q: What are the factor combinations of the number 12,090,407?

 A:
Positive:   1 x 120904077 x 172720149 x 246743101 x 119707343 x 35249349 x 34643707 x 171012443 x 4949
Negative: -1 x -12090407-7 x -1727201-49 x -246743-101 x -119707-343 x -35249-349 x -34643-707 x -17101-2443 x -4949


How do I find the factor combinations of the number 12,090,407?

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 12,090,407, 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 12,090,407
-1 -12,090,407

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 12,090,407.

Example:
1 x 12,090,407 = 12,090,407
and
-1 x -12,090,407 = 12,090,407
Notice both answers equal 12,090,407

With that explanation out of the way, let's continue. Next, we take the number 12,090,407 and divide it by 2:

12,090,407 ÷ 2 = 6,045,203.5

If the quotient is a whole number, then 2 and 6,045,203.5 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 12,090,407
-1 -12,090,407

Now, we try dividing 12,090,407 by 3:

12,090,407 ÷ 3 = 4,030,135.6667

If the quotient is a whole number, then 3 and 4,030,135.6667 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 12,090,407
-1 -12,090,407

Let's try dividing by 4:

12,090,407 ÷ 4 = 3,022,601.75

If the quotient is a whole number, then 4 and 3,022,601.75 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 12,090,407
-1 12,090,407
Keep dividing by the next highest number until you cannot divide anymore.

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

17491013433497072,4434,94917,10134,64335,249119,707246,7431,727,20112,090,407
-1-7-49-101-343-349-707-2,443-4,949-17,101-34,643-35,249-119,707-246,743-1,727,201-12,090,407

More Examples

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