Q: What are the factor combinations of the number 12,001,165?

 A:
Positive:   1 x 120011655 x 240023311 x 109101555 x 218203113 x 106205565 x 212411243 x 96551931 x 6215
Negative: -1 x -12001165-5 x -2400233-11 x -1091015-55 x -218203-113 x -106205-565 x -21241-1243 x -9655-1931 x -6215


How do I find the factor combinations of the number 12,001,165?

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 12,001,165, 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 12,001,165
-1 -12,001,165

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 12,001,165.

Example:
1 x 12,001,165 = 12,001,165
and
-1 x -12,001,165 = 12,001,165
Notice both answers equal 12,001,165

With that explanation out of the way, let's continue. Next, we take the number 12,001,165 and divide it by 2:

12,001,165 ÷ 2 = 6,000,582.5

If the quotient is a whole number, then 2 and 6,000,582.5 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 12,001,165
-1 -12,001,165

Now, we try dividing 12,001,165 by 3:

12,001,165 ÷ 3 = 4,000,388.3333

If the quotient is a whole number, then 3 and 4,000,388.3333 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 12,001,165
-1 -12,001,165

Let's try dividing by 4:

12,001,165 ÷ 4 = 3,000,291.25

If the quotient is a whole number, then 4 and 3,000,291.25 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 12,001,165
-1 12,001,165
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551135651,2431,9316,2159,65521,241106,205218,2031,091,0152,400,23312,001,165
-1-5-11-55-113-565-1,243-1,931-6,215-9,655-21,241-106,205-218,203-1,091,015-2,400,233-12,001,165

More Examples

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