Q: What are the factor combinations of the number 688,608?

How do I find the factor combinations of the number 688,608?

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 688,608, 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		688,608
-1		-688,608

With that explanation out of the way, let's continue. Next, we take the number 688,608 and divide it by 2:

688,608 ÷ 2 = 344,304

If the quotient is a whole number, then 2 and 344,304 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:

Now, we try dividing 688,608 by 3:

688,608 ÷ 3 = 229,536

If the quotient is a whole number, then 3 and 229,536 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:

Let's try dividing by 4:

688,608 ÷ 4 = 172,152

If the quotient is a whole number, then 4 and 172,152 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:

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

More Examples

Here are some more numbers to try:

Try the factor calculator