Q: What are the factor combinations of the number 13,131,223?

 A:
Positive:   1 x 131312237 x 187588919 x 691117133 x 98731
Negative: -1 x -13131223-7 x -1875889-19 x -691117-133 x -98731


How do I find the factor combinations of the number 13,131,223?

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 13,131,223, 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 13,131,223
-1 -13,131,223

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 13,131,223.

Example:
1 x 13,131,223 = 13,131,223
and
-1 x -13,131,223 = 13,131,223
Notice both answers equal 13,131,223

With that explanation out of the way, let's continue. Next, we take the number 13,131,223 and divide it by 2:

13,131,223 ÷ 2 = 6,565,611.5

If the quotient is a whole number, then 2 and 6,565,611.5 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 13,131,223
-1 -13,131,223

Now, we try dividing 13,131,223 by 3:

13,131,223 ÷ 3 = 4,377,074.3333

If the quotient is a whole number, then 3 and 4,377,074.3333 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 13,131,223
-1 -13,131,223

Let's try dividing by 4:

13,131,223 ÷ 4 = 3,282,805.75

If the quotient is a whole number, then 4 and 3,282,805.75 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 13,131,223
-1 13,131,223
Keep dividing by the next highest number until you cannot divide anymore.

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

171913398,731691,1171,875,88913,131,223
-1-7-19-133-98,731-691,117-1,875,889-13,131,223

More Examples

Here are some more numbers to try:

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