18.3 Example Using Recursion: Factorials

Let’s write a recursive program to perform a popular mathematical calculation. Consider the factorial of a positive integer n, written n! (pronounced “n factorial”), which is the product


with 1! equal to 1 and 0! defined to be 1. For example, 5! is the product 54321, which is equal to 120.

The factorial of integer number (where number 0) can be calculated iteratively (non-recursively) using a for statement as follows:

factorial = 1;
for (int counter = number; counter >= 1; counter--) {
   factorial *= counter;

A recursive declaration of the factorial calculation for integers greater than 1 is arrived at by observing the following relationship:


For example, 5! is clearly ...

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