Factorial on Calculator

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Factorial Calculator

function calculateFactorial() { var inputNum = document.getElementById("inputNumber").value; var num = parseInt(inputNum); var resultDiv = document.getElementById("result"); if (isNaN(num) || !Number.isInteger(num) || num < 0) { resultDiv.innerHTML = "Please enter a valid non-negative integer."; return; } if (num === 0) { resultDiv.innerHTML = "The factorial of 0 (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.toLocaleString() + ""; }

Understanding the Factorial Function

The factorial function, 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. It's a fundamental concept in combinatorics, probability, and various areas of mathematics and computer science.

What is a Factorial?

In simple terms, the factorial of a non-negative integer 'n' is the product of all positive integers less than or equal to 'n'.

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. This definition is crucial for many mathematical formulas to hold true, especially in combinatorics.

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

Applications of Factorials

Factorials are not just abstract mathematical concepts; they have practical applications in various fields:

  • Combinatorics: They are used to calculate the number of ways to arrange a set of distinct items (permutations). For example, if you have 5 different books, there are 5! = 120 ways to arrange them on a shelf.
  • Probability: Factorials are essential in calculating probabilities, especially when dealing with permutations and combinations.
  • Series Expansions: Many important mathematical functions, like the exponential function (e^x) and trigonometric functions (sin x, cos x), can be expressed using infinite series that involve factorials.
  • Computer Science: They appear in algorithms for sorting, searching, and other computational problems.

How to Use the Factorial Calculator

Our Factorial Calculator makes it easy to find the factorial of any non-negative integer:

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

Remember, factorials grow very rapidly. Even relatively small numbers can result in very large factorials. For instance, 20! is already a massive number. Our calculator handles these large numbers as accurately as JavaScript's number type allows.

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