Q: What are the factor combinations of the number 12,164,401?

 A:
Positive:   1 x 1216440117 x 71555323 x 52888753 x 229517391 x 31111587 x 20723901 x 135011219 x 9979
Negative: -1 x -12164401-17 x -715553-23 x -528887-53 x -229517-391 x -31111-587 x -20723-901 x -13501-1219 x -9979


How do I find the factor combinations of the number 12,164,401?

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 12,164,401, 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 12,164,401
-1 -12,164,401

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 12,164,401.

Example:
1 x 12,164,401 = 12,164,401
and
-1 x -12,164,401 = 12,164,401
Notice both answers equal 12,164,401

With that explanation out of the way, let's continue. Next, we take the number 12,164,401 and divide it by 2:

12,164,401 ÷ 2 = 6,082,200.5

If the quotient is a whole number, then 2 and 6,082,200.5 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 12,164,401
-1 -12,164,401

Now, we try dividing 12,164,401 by 3:

12,164,401 ÷ 3 = 4,054,800.3333

If the quotient is a whole number, then 3 and 4,054,800.3333 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 12,164,401
-1 -12,164,401

Let's try dividing by 4:

12,164,401 ÷ 4 = 3,041,100.25

If the quotient is a whole number, then 4 and 3,041,100.25 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 12,164,401
-1 12,164,401
Keep dividing by the next highest number until you cannot divide anymore.

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

11723533915879011,2199,97913,50120,72331,111229,517528,887715,55312,164,401
-1-17-23-53-391-587-901-1,219-9,979-13,501-20,723-31,111-229,517-528,887-715,553-12,164,401

More Examples

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