Calculating Factorials

Factorial Calculator

function calculateFactorial() { var inputNumber = document.getElementById("factorialNumber").value; var num = parseInt(inputNumber); var resultDiv = document.getElementById("factorialResult"); if (isNaN(num) || inputNumber.trim() === "") { resultDiv.innerHTML = "Please enter a valid number."; return; } if (num < 0) { resultDiv.innerHTML = "Factorial is not defined for negative numbers."; return; } if (num !== parseFloat(inputNumber)) { resultDiv.innerHTML = "Please enter a whole number (integer)."; return; } if (num === 0) { resultDiv.innerHTML = "The factorial of " + num + " (0!) is: 1"; return; } var factorial = 1; for (var i = 1; i <= num; i++) { factorial *= i; } resultDiv.innerHTML = "The factorial of " + num + " (" + num + "!) is: " + factorial + ""; }

Understanding Factorials

A factorial, denoted by an exclamation mark (n!), is a mathematical operation that multiplies a given non-negative integer by all the positive integers less than it. In simpler terms, it's the product of an integer and all the integers below it down to 1.

The Formula

The formula for a factorial is:

n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1

There's a special case: the factorial of 0 (0!) is defined as 1.

Examples of Factorials

• 0! = 1 (by definition)
• 1! = 1
• 2! = 2 × 1 = 2
• 3! = 3 × 2 × 1 = 6
• 4! = 4 × 3 × 2 × 1 = 24
• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

How to Use This Calculator

Our Factorial Calculator makes it easy to find the factorial of any non-negative integer. Simply follow these steps:

1. Enter a Number: In the input field labeled "Enter a non-negative integer:", type the whole number for which you want to calculate the factorial.
2. Click Calculate: Press the "Calculate Factorial" button.
3. View Result: The calculator will instantly display the factorial of your entered number in the result area.

The calculator will also provide helpful messages if you enter a negative number, a decimal, or non-numeric input.

Applications of Factorials

Factorials are fundamental in various fields of mathematics and science, particularly in:

• Combinatorics: They are used to count the number of ways to arrange items (permutations) or select items (combinations). For example, the number of ways to arrange 5 distinct books on a shelf is 5!.
• Probability: Factorials are crucial for calculating probabilities in scenarios involving arrangements and selections.
• Calculus: They appear in Taylor series expansions and other advanced mathematical concepts.
• Computer Science: Used in algorithms for sorting, searching, and generating permutations.

Whether you're a student, a mathematician, or just curious, this calculator provides a quick and accurate way to compute factorials.