Q: What are the factor combinations of the number 420,668?

How do I find the factor combinations of the number 420,668?

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 420,668, 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		420,668
-1		-420,668

With that explanation out of the way, let's continue. Next, we take the number 420,668 and divide it by 2:

420,668 ÷ 2 = 210,334

If the quotient is a whole number, then 2 and 210,334 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 420,668 by 3:

420,668 ÷ 3 = 140,222.6667

If the quotient is a whole number, then 3 and 140,222.6667 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:

Let's try dividing by 4:

420,668 ÷ 4 = 105,167

If the quotient is a whole number, then 4 and 105,167 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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