How do I find the factor combinations of the number 363,904?
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 363,904, 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.
Why are the negative numbers included?
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 363,904.
Example:
1 x 363,904 = 363,904
and
-1 x -363,904 = 363,904
Notice both answers equal 363,904
With that explanation out of the way, let's continue. Next, we take the number 363,904 and divide it by 2:
363,904 ÷ 2 = 181,952
If the quotient is a whole number, then 2 and 181,952 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 363,904 by 3:
363,904 ÷ 3 = 121,301.3333
If the quotient is a whole number, then 3 and 121,301.3333 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:
363,904 ÷ 4 = 90,976
If the quotient is a whole number, then 4 and 90,976 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:
Keep dividing by the next highest number until you cannot divide anymore.
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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