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

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

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, 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
-1		-688

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

688 ÷ 2 = 344

If the quotient is a whole number, then 2 and 344 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 by 3:

688 ÷ 3 = 229.3333

If the quotient is a whole number, then 3 and 229.3333 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:

Let's try dividing by 4:

688 ÷ 4 = 172

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

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