Factorial of a Number

Program to calculate factorial of a number

BeginnerTopic: Loop Programs
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JavaScript Factorial of a Number Program

This program helps you to learn the fundamental structure and syntax of JavaScript programming.

Try This Code
// Factorial: n! = n × (n-1) × (n-2) × ... × 2 × 1
// Example: 5! = 5 × 4 × 3 × 2 × 1 = 120

// Method 1: Using for loop
function factorialLoop(n) {
    if (n < 0) return "Invalid input";
    if (n === 0 || n === 1) return 1;
    
    let result = 1;
    for (let i = 2; i <= n; i++) {
        result *= i;
    }
    return result;
}

console.log("5! =", factorialLoop(5));
console.log("0! =", factorialLoop(0));
console.log("10! =", factorialLoop(10));

// Method 2: Using recursion
function factorialRecursive(n) {
    if (n < 0) return "Invalid input";
    if (n === 0 || n === 1) return 1;
    return n * factorialRecursive(n - 1);
}

console.log("\nUsing recursion:");
console.log("5! =", factorialRecursive(5));
console.log("7! =", factorialRecursive(7));

// Method 3: Using while loop
function factorialWhile(n) {
    if (n < 0) return "Invalid input";
    if (n === 0 || n === 1) return 1;
    
    let result = 1;
    let i = n;
    while (i > 1) {
        result *= i;
        i--;
    }
    return result;
}

console.log("\nUsing while:");
console.log("6! =", factorialWhile(6));

// Method 4: Using reduce
function factorialReduce(n) {
    if (n < 0) return "Invalid input";
    if (n === 0 || n === 1) return 1;
    
    return Array.from({length: n}, (_, i) => i + 1)
                .reduce((product, num) => product * num, 1);
}

console.log("\nUsing reduce:");
console.log("4! =", factorialReduce(4));
Output
5! = 120
0! = 1
10! = 3628800

Using recursion:
5! = 120
7! = 5040

Using while:
6! = 720

Using reduce:
4! = 24

Understanding Factorial of a Number

This program demonstrates different approaches to calculate factorial.

Factorial Definition

n! = n × (n-1) × (n-2) × ... × 2 × 1

Special Cases:

•0! = 1
•1! = 1
•Negative numbers: Invalid

Method 1: For Loop

Iterative approach:

let result = 1;
for (let i = 2; i <= n; i++) {
    result *= i;
}

Pros:

•Easy to understand
•Efficient
•No stack overflow risk

Method 2: Recursion

Function calls itself:

function factorial(n) {
    if (n <= 1) return 1;
}

    return n * factorial(n - 1);

How Recursion Works:

1.Base case: n <= 1 returns 1
2.Recursive case: n * factorial(n-1)
3.Unwinds: multiplies results back up

Example: factorial(5)

•factorial(5) = 5 × factorial(4)
•factorial(4) = 4 × factorial(3)
•factorial(3) = 3 × factorial(2)
•factorial(2) = 2 × factorial(1)
•factorial(1) = 1
•Unwinds: 1 × 2 × 3 × 4 × 5 = 120

Pros:

•Elegant code
•Matches mathematical definition

Cons:

•Stack overflow for large numbers
•Less efficient than loop

Method 3: While Loop

Decrementing counter:

while (i > 1) {
    result *= i;
    i--;
}

Method 4: Reduce (Functional)

Using array methods:

Array.from({length: n}, (_, i) => i + 1)
     .reduce((product, num) => product * num, 1);

Edge Cases:

•Negative numbers: Invalid
•0: Returns 1
•Large numbers: May overflow

When to Use:

-

Loop

: Production code, large numbers

-

Recursion

: Learning, small numbers

-

Reduce

: Functional style

Let us now understand every line and the components of the above program.

Note: To write and run JavaScript programs, you need to set up the local environment on your computer. Refer to the complete article Setting up JavaScript Development Environment. If you do not want to set up the local environment on your computer, you can also use online IDE to write and run your JavaScript programs.

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Reverse a Number
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Sum of n Natural Numbers
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Reverse a Number

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