Q: What are the factor combinations of the number 12,236,209?

 A:
Positive:   1 x 1223620917 x 71977719 x 64401143 x 284563323 x 37883731 x 16739817 x 14977881 x 13889
Negative: -1 x -12236209-17 x -719777-19 x -644011-43 x -284563-323 x -37883-731 x -16739-817 x -14977-881 x -13889


How do I find the factor combinations of the number 12,236,209?

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 12,236,209, 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 12,236,209
-1 -12,236,209

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 12,236,209.

Example:
1 x 12,236,209 = 12,236,209
and
-1 x -12,236,209 = 12,236,209
Notice both answers equal 12,236,209

With that explanation out of the way, let's continue. Next, we take the number 12,236,209 and divide it by 2:

12,236,209 ÷ 2 = 6,118,104.5

If the quotient is a whole number, then 2 and 6,118,104.5 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 12,236,209
-1 -12,236,209

Now, we try dividing 12,236,209 by 3:

12,236,209 ÷ 3 = 4,078,736.3333

If the quotient is a whole number, then 3 and 4,078,736.3333 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 12,236,209
-1 -12,236,209

Let's try dividing by 4:

12,236,209 ÷ 4 = 3,059,052.25

If the quotient is a whole number, then 4 and 3,059,052.25 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 12,236,209
-1 12,236,209
Keep dividing by the next highest number until you cannot divide anymore.

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

117194332373181788113,88914,97716,73937,883284,563644,011719,77712,236,209
-1-17-19-43-323-731-817-881-13,889-14,977-16,739-37,883-284,563-644,011-719,777-12,236,209

More Examples

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