Calculate Factorial

Factorial Calculator

function calculateFactorialResult() { var inputVal = document.getElementById("numberInput").value; var resultBox = document.getElementById("factorial-result-box"); var output = document.getElementById("factorial-output"); var formula = document.getElementById("factorial-formula"); if (inputVal === "" || inputVal 170) { // Standard JS Numbers cap at 170! (Infinity) // Using BigInt for larger numbers try { var fact = BigInt(1); for (var i = 1; i <= n; i++) { fact = fact * BigInt(i); } resultBox.style.display = "block"; output.innerHTML = "" + n + "! = " + fact.toString(); formula.innerHTML = "Calculated using BigInt precision."; } catch (e) { output.innerHTML = "Error: Number too large to process."; } } else { var fact = 1; for (var i = 1; i <= n; i++) { fact *= i; } resultBox.style.display = "block"; output.innerHTML = "" + n + "! = " + fact.toLocaleString(); if (n 0) { var sequence = []; for (var j = n; j >= 1; j–) { sequence.push(j); } formula.innerHTML = "Calculation: " + sequence.join(" × "); } else if (n === 0) { formula.innerHTML = "By definition, 0! is 1."; } else { formula.innerHTML = "The product of all integers from 1 to " + n + "."; } } }

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What is a Factorial?

In mathematics, the factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted by the symbol n! (read as "n factorial"). For example, 5! is equal to 120 (5 × 4 × 3 × 2 × 1).

The Factorial Formula

The general formula for calculating a factorial is:

n! = n × (n – 1) × (n – 2) × … × 3 × 2 × 1

A special rule applies to zero: 0! = 1. While this may seem counterintuitive, it is a mathematical convention that simplifies many formulas in combinatorics and calculus.

Real-World Examples of Factorials

Factorials are vital in the field of combinatorics, which deals with counting the number of ways things can be arranged or selected. Here are two practical examples:

• Permutations: If you have 5 books and want to know how many different ways you can arrange them on a shelf, the answer is 5! (120 ways).
• Card Games: The number of possible ways to arrange a standard 52-card deck is 52!. This number is so large (8.06 × 10⁶⁷) that it is virtually certain no two shuffled decks in history have ever been exactly the same.

Factorial Table (1-10)

Number (n)	Factorial (n!)
1	1
2	2
3	6
4	24
5	120
6	720
7	5,040
8	40,320
9	362,880
10	3,628,800

Frequently Asked Questions

Q: Why is 0! equal to 1?
A: It is defined this way to ensure that formulas for combinations and permutations work correctly. It also relates to the empty product—the result of multiplying no numbers at all is 1.

Q: Can you find the factorial of a decimal?
A: The standard factorial only applies to integers. However, the Gamma Function extends the concept of factorials to complex and real numbers (excluding negative integers).

Q: How fast do factorials grow?
A: Extremely fast! While 10! is only 3.6 million, 20! is over 2.4 quintillion. This is known as "factorial growth," which is even faster than exponential growth.