Q: What are the factor combinations of the number 686,412?

How do I find the factor combinations of the number 686,412?

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 686,412, 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		686,412
-1		-686,412

With that explanation out of the way, let's continue. Next, we take the number 686,412 and divide it by 2:

686,412 ÷ 2 = 343,206

If the quotient is a whole number, then 2 and 343,206 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 686,412 by 3:

686,412 ÷ 3 = 228,804

If the quotient is a whole number, then 3 and 228,804 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:

686,412 ÷ 4 = 171,603

If the quotient is a whole number, then 4 and 171,603 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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