Q: What are the factor combinations of the number 311,729?

 A:
Positive:   1 x 31172911 x 2833917 x 18337187 x 1667
Negative: -1 x -311729-11 x -28339-17 x -18337-187 x -1667


How do I find the factor combinations of the number 311,729?

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 311,729, 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.

1 311,729
-1 -311,729

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 311,729.

Example:
1 x 311,729 = 311,729
and
-1 x -311,729 = 311,729
Notice both answers equal 311,729

With that explanation out of the way, let's continue. Next, we take the number 311,729 and divide it by 2:

311,729 ÷ 2 = 155,864.5

If the quotient is a whole number, then 2 and 155,864.5 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:

1 311,729
-1 -311,729

Now, we try dividing 311,729 by 3:

311,729 ÷ 3 = 103,909.6667

If the quotient is a whole number, then 3 and 103,909.6667 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:

1 311,729
-1 -311,729

Let's try dividing by 4:

311,729 ÷ 4 = 77,932.25

If the quotient is a whole number, then 4 and 77,932.25 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:

1 311,729
-1 311,729
Keep dividing by the next highest number until you cannot divide anymore.

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

111171871,66718,33728,339311,729
-1-11-17-187-1,667-18,337-28,339-311,729

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 311,729:


Ask a Question