In math we can take the factorial of an integer by taking the product of its preceding positive integers. So:

1! = 1
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
5! = 5 * 4 * 3 * 2 * 1 = 120

We could change the notation of the above and replace the exclamation point (!) with a function called factorial such that:

factorial(5) = 5!

and thus:

factorial(5) = 5 * 4 * 3 * 2 * 1 = 120

To complete this exercise you must:

• Create a file in "public_html/php" called "factorial.php".
• Be sure that "factorial.php" is viewable from the web.
• Fill in "factorial.php" with this incomplete code.
• Define a function which takes in a number $n and returns factorial($n).
• Call your function on the number 5 and print the result.

For extra credit make a recursive version of your factorial function. Use the following definition:

n! =

HINTS:

If you are not sure where to start here are some hints for the exercise (these hints are not for the extra credit).

• Use a loop to define your function
• Try making your loop count backwards ($i-- instead of $i++)
• Try defining a variable which you will return and set the the variable equal to one. Then use your loop to multiply it by the descending values of $n.