Q: What are the factor combinations of the number 520,658?

 A:
Positive:   1 x 5206582 x 260329
Negative: -1 x -520658-2 x -260329


How do I find the factor combinations of the number 520,658?

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 520,658, 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.

1 520,658
-1 -520,658

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 520,658.

Example:
1 x 520,658 = 520,658
and
-1 x -520,658 = 520,658
Notice both answers equal 520,658

With that explanation out of the way, let's continue. Next, we take the number 520,658 and divide it by 2:

520,658 ÷ 2 = 260,329

If the quotient is a whole number, then 2 and 260,329 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 260,329 520,658
-1 -2 -260,329 -520,658

Now, we try dividing 520,658 by 3:

520,658 ÷ 3 = 173,552.6667

If the quotient is a whole number, then 3 and 173,552.6667 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 2 260,329 520,658
-1 -2 -260,329 -520,658

Let's try dividing by 4:

520,658 ÷ 4 = 130,164.5

If the quotient is a whole number, then 4 and 130,164.5 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 2 260,329 520,658
-1 -2 -260,329 520,658
Keep dividing by the next highest number until you cannot divide anymore.

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

12260,329520,658
-1-2-260,329-520,658

More Examples

Here are some more numbers to try:

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