Q: What are the factor combinations of the number 196,768?

How do I find the factor combinations of the number 196,768?

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 196,768, 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		196,768
-1		-196,768

With that explanation out of the way, let's continue. Next, we take the number 196,768 and divide it by 2:

196,768 ÷ 2 = 98,384

If the quotient is a whole number, then 2 and 98,384 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 196,768 by 3:

196,768 ÷ 3 = 65,589.3333

If the quotient is a whole number, then 3 and 65,589.3333 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:

196,768 ÷ 4 = 49,192

If the quotient is a whole number, then 4 and 49,192 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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