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Function to compute factorial of a number in JavaScript
In this article, we will explore different methods to calculate the factorial of a number in JavaScript.
What is Factorial?
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. For example, the factorial of 4 is 4 × 3 × 2 × 1 = 24, represented as 4!.
The value of 0! is defined as 1 by convention.
Mathematical Formula
The factorial of n is represented as n! and calculated using:
n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
Using For Loop
We can calculate factorial using a for loop by iterating from n down to 1.
Algorithm
Initialize a result variable with value 1
If number is less than 0, return -1 (factorial undefined for negative numbers)
If number equals 0, return 1
For numbers greater than 0, multiply result by each number from n down to 1
<!DOCTYPE html>
<html>
<head>
<title>Factorial using For Loop</title>
</head>
<body>
<button onClick="calculateFactorial()">Calculate Factorial</button>
<p id="result"></p>
<script>
function calculateFactorial() {
function factorial(num) {
if (num < 0) {
return -1;
}
else if (num === 0) {
return 1;
}
else {
let result = 1;
for (let i = num; i > 1; i--) {
result *= i;
}
return result;
}
}
const num = 5;
const factorialResult = factorial(num);
document.getElementById("result").innerHTML = `Factorial of ${num} is: ${factorialResult}`;
}
</script>
</body>
</html>
Factorial of 5 is: 120
Using Recursion
Recursion provides an elegant solution by calling the function itself with decremented values until reaching the base case.
Algorithm
If number is less than 0, return -1
If number equals 0, return 1 (base case)
Otherwise, return num × factorial(num - 1)
<!DOCTYPE html>
<html>
<head>
<title>Factorial using Recursion</title>
</head>
<body>
<button onClick="calculateRecursiveFactorial()">Calculate Factorial</button>
<p id="recursiveResult"></p>
<script>
function calculateRecursiveFactorial() {
function factorial(num) {
if (num < 0) {
return -1;
}
else if (num === 0) {
return 1;
}
else {
return num * factorial(num - 1);
}
}
const num = 5;
const result = factorial(num);
document.getElementById("recursiveResult").innerHTML = `Factorial of ${num} using recursion: ${result}`;
}
</script>
</body>
</html>
Factorial of 5 using recursion: 120
Using While Loop
A while loop provides another iterative approach to calculate factorial.
Algorithm
Initialize result variable with the input number
Handle special cases: 0! = 1, 1! = 1
Use while loop to multiply result by decremented values
<!DOCTYPE html>
<html>
<head>
<title>Factorial using While Loop</title>
</head>
<body>
<button onClick="calculateWhileFactorial()">Calculate Factorial</button>
<p id="whileResult"></p>
<script>
function calculateWhileFactorial() {
function factorial(num) {
if (num < 0) {
return -1;
}
if (num === 0 || num === 1) {
return 1;
}
let result = num;
while (num > 1) {
num--;
result *= num;
}
return result;
}
const num = 5;
const result = factorial(num);
document.getElementById("whileResult").innerHTML = `Factorial of ${num} using while loop: ${result}`;
}
</script>
</body>
</html>
Factorial of 5 using while loop: 120
Comparison of Methods
| Method | Time Complexity | Space Complexity | Readability |
|---|---|---|---|
| For Loop | O(n) | O(1) | Good |
| Recursion | O(n) | O(n) | Excellent |
| While Loop | O(n) | O(1) | Good |
Conclusion
All three methods effectively calculate factorial with O(n) time complexity. Choose recursion for mathematical elegance, or iterative approaches (for/while loops) for better memory efficiency in large computations.
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