Q: What are the factor combinations of the number 12,100,369?

 A:
Positive:   1 x 1210036923 x 52610337 x 32703759 x 205091241 x 50209851 x 142191357 x 89172183 x 5543
Negative: -1 x -12100369-23 x -526103-37 x -327037-59 x -205091-241 x -50209-851 x -14219-1357 x -8917-2183 x -5543


How do I find the factor combinations of the number 12,100,369?

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 12,100,369, 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 12,100,369
-1 -12,100,369

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 12,100,369.

Example:
1 x 12,100,369 = 12,100,369
and
-1 x -12,100,369 = 12,100,369
Notice both answers equal 12,100,369

With that explanation out of the way, let's continue. Next, we take the number 12,100,369 and divide it by 2:

12,100,369 ÷ 2 = 6,050,184.5

If the quotient is a whole number, then 2 and 6,050,184.5 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 12,100,369
-1 -12,100,369

Now, we try dividing 12,100,369 by 3:

12,100,369 ÷ 3 = 4,033,456.3333

If the quotient is a whole number, then 3 and 4,033,456.3333 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 12,100,369
-1 -12,100,369

Let's try dividing by 4:

12,100,369 ÷ 4 = 3,025,092.25

If the quotient is a whole number, then 4 and 3,025,092.25 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 12,100,369
-1 12,100,369
Keep dividing by the next highest number until you cannot divide anymore.

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

12337592418511,3572,1835,5438,91714,21950,209205,091327,037526,10312,100,369
-1-23-37-59-241-851-1,357-2,183-5,543-8,917-14,219-50,209-205,091-327,037-526,103-12,100,369

More Examples

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