Factorial in Calculator

Factorial Calculator

function calculateFactorial() { var inputNum = document.getElementById("inputNumber").value; var num = parseInt(inputNum); var resultDiv = document.getElementById("factorialResult"); if (isNaN(num) || !Number.isInteger(num)) { resultDiv.innerHTML = "Please enter a valid integer."; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.borderColor = '#f5c6cb'; resultDiv.style.color = '#721c24'; return; } if (num < 0) { resultDiv.innerHTML = "Factorial is not defined for negative numbers."; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.borderColor = '#f5c6cb'; resultDiv.style.color = '#721c24'; return; } if (num === 0) { resultDiv.innerHTML = "The factorial of 0 (0!) is: 1"; resultDiv.style.backgroundColor = '#d4edda'; resultDiv.style.borderColor = '#c3e6cb'; resultDiv.style.color = '#155724'; return; } var factorial = 1; for (var i = 1; i <= num; i++) { factorial *= i; } resultDiv.innerHTML = "The factorial of " + num + " (" + num + "!) is: " + factorial; resultDiv.style.backgroundColor = '#d4edda'; resultDiv.style.borderColor = '#c3e6cb'; resultDiv.style.color = '#155724'; } // Initial calculation on page load for the default value window.onload = calculateFactorial;

Understanding the Factorial Function

The factorial function, denoted by an exclamation mark (n!), is a mathematical operation that multiplies a given non-negative integer n by all the positive integers less than it. It's a fundamental concept in combinatorics, probability, and various areas of mathematics and computer science.

How is Factorial Calculated?

For any positive integer n, the factorial is calculated as:

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

There's a special case for 0! (zero factorial), which is defined as 1. This definition is crucial for many mathematical formulas to hold true, especially in combinatorics.

Examples of Factorial Calculations:

• 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

Applications of Factorials:

Factorials appear in many different fields:

• Combinatorics: They are used to calculate the number of ways to arrange a set of distinct items (permutations). For example, the number of ways to arrange 5 different books on a shelf is 5! = 120.
• Probability: Factorials are essential in probability theory, particularly when calculating the likelihood of specific sequences of events.
• Series Expansions: Many important mathematical functions, like the exponential function (e^x) and trigonometric functions (sin(x), cos(x)), have Taylor series expansions that involve factorials.
• Computer Science: Factorials are often used in algorithms related to permutations, combinations, and in analyzing the complexity of certain sorting algorithms.

Our Factorial Calculator provides a quick and easy way to compute the factorial of any non-negative integer, helping you understand and apply this fundamental mathematical concept.