Factorial of a Number (JavaScript)

The factorial of a non-negative integer ‘n’, denoted as n!, is the product of all positive integers less than or equal to ‘n’. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120. The factorial of 0 (0!) is defined as 1.

The factorial function grows very rapidly. It’s a classic problem used to illustrate both iterative and recursive programming.

$$n! = n times (n-1) times (n-2) times ldots times 1$$

And specifically, $$0! = 1$$

This is generally the most straightforward and efficient way to calculate factorial for common integer sizes, as it avoids the overhead of recursion.

Explanation:

• Handles invalid input (negative numbers) and the base case for 0.
• Initializes `result` to 1.
• Multiplies `result` by each integer from 1 up to `n`.

The factorial definition lends itself well to recursion, where a function calls itself. This can be more elegant but might be less efficient for very large `n` due to function call overhead and potential stack overflow issues.

Explanation:

• Base Case: When `n` is 0, the function returns 1, stopping the recursion.
• Recursive Step: For any `n > 0`, it returns `n` multiplied by the factorial of `n-1`. This continues until the base case is reached, and then the results are multiplied back up the call stack.

Be aware that JavaScript uses 64-bit floating-point numbers for all number types. The maximum safe integer in JavaScript is `Number.MAX_SAFE_INTEGER` which is 253 - 1. Factorials beyond 20! will exceed this limit and produce inexact results or `Infinity`. For very large factorials, you would need to use a BigInt library or JavaScript's native BigInt type (if only positive results are needed and the environment supports it).

• Iterative vs. Recursive: Both are valid, with iterative often preferred for performance and avoiding stack limits. Recursion can be more elegant for problems with a natural recursive definition.
• Base Case: Absolutely critical for recursive functions to prevent infinite loops.
• Data Type Limits: Be mindful of JavaScript's number precision limitations for large factorial calculations and consider using `BigInt` for very large results.