added recursive factorial function in java

code/languages/Java/Factorial.java

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+import java.util.Scanner;
+
+class Factorial {
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+        System.out.print("Enter a number to find its factorial: ");
+        int n = sc.nextInt();
+
+        // Try to calculate the factorial of n, catch any exceptions that are thrown.
+        try {
+            System.out.println(n + "! = " + factorial(n));
+        } catch (Exception e) {
+            System.out.println(e.getMessage());
+        }
+        sc.close();
+    }
+
+    /**
+     * This method recursively calculates the factorial of an integer. 
+     * @param n An integer we are finding the factorial of.
+     * @return The factorial of `n`.
+     * @throws Exception If `n` is negative.
+     */
+    public static int factorial(int n) throws Exception {
+
+        // Check that factorial is non-negative, throw an expection if not.
+        if (n < 0) {
+            throw new Exception("Factorial of negative number is not possible");
+        } else if (n == 0 || n == 1) { // Base cases, no need to recurse further.
+            return 1;
+        } else { // Non-negative n and not at a base case, so multiply n by the factorial of n-1 and return it.
+            return n * factorial(n - 1);
+        }
+    }
+}

code/languages/Java/README_Factorial.md

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+# Recursive Factorial
+
+This program shows how we can calculate any integer factorial recursively. A factorial is defined 
+as $n! = (n) \cdot (n-1) \cdot (n-2) \cdots (2) \cdot (1)$. So, we can rewrite this as $n! = (n) \cdot (n-1)!$ 
+with base cases of $1! = 1$ and $0! = 1$. This is our recursive definition and is how we implement 
+the code.
+
+## Features
+
+- **Factorial Calculation**: The program calculates the factorial of a non-negative integer.
+- **Exception Handling**: Throws an exception when trying to compute the factorial of a negative number.\
+
+## Getting Started
+
+### Running the Program
+
+1. Clone this repository to your local machine.
+2. Compile and run the `Factorial` class.
+
+### Warning
+
+Be aware that factorials grow extremely quickly. So, there is a limit to how large the input 
+$n$ can be without causing overflow, leading to an incorrect answer.