Q: What are the factor combinations of the number 173,172?

How do I find the factor combinations of the number 173,172?

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 173,172, 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		173,172
-1		-173,172

With that explanation out of the way, let's continue. Next, we take the number 173,172 and divide it by 2:

173,172 ÷ 2 = 86,586

If the quotient is a whole number, then 2 and 86,586 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 173,172 by 3:

173,172 ÷ 3 = 57,724

If the quotient is a whole number, then 3 and 57,724 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:

173,172 ÷ 4 = 43,293

If the quotient is a whole number, then 4 and 43,293 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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