Q: What are the factor combinations of the number 518,723?

 A:
Positive:   1 x 51872329 x 1788731 x 16733577 x 899
Negative: -1 x -518723-29 x -17887-31 x -16733-577 x -899


How do I find the factor combinations of the number 518,723?

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 518,723, 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.

1 518,723
-1 -518,723

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 518,723.

Example:
1 x 518,723 = 518,723
and
-1 x -518,723 = 518,723
Notice both answers equal 518,723

With that explanation out of the way, let's continue. Next, we take the number 518,723 and divide it by 2:

518,723 ÷ 2 = 259,361.5

If the quotient is a whole number, then 2 and 259,361.5 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:

1 518,723
-1 -518,723

Now, we try dividing 518,723 by 3:

518,723 ÷ 3 = 172,907.6667

If the quotient is a whole number, then 3 and 172,907.6667 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:

1 518,723
-1 -518,723

Let's try dividing by 4:

518,723 ÷ 4 = 129,680.75

If the quotient is a whole number, then 4 and 129,680.75 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:

1 518,723
-1 518,723
Keep dividing by the next highest number until you cannot divide anymore.

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

1293157789916,73317,887518,723
-1-29-31-577-899-16,733-17,887-518,723

More Examples

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