# Factorial Calculator (n!)

Instructions:
• Enter a non-negative integer in the input field.
• Click "Calculate Factorial" to calculate the factorial.
• View the result, detailed calculation, and formula.
• Your calculation history will be displayed below.
• Click "Clear Results" to reset the results and history.
• Click "Copy Results" to copy the result and explanation to the clipboard.
Calculation History:

## What is Factorial?

In mathematics, the factorial of a non-negative integer “n,” denoted as “n!”, is the product of all positive integers from 1 to “n.” It is a fundamental mathematical operation used in various mathematical and combinatorial calculations. The factorial of 0 is defined to be 1 by convention.

## All Formulae Related to Factorial

1. Factorial Formula:
• The factorial of a non-negative integer “n” is calculated as follows: n! = n × (n - 1) × (n - 2) × ... × 3 × 2 × 1
2. Factorial of 0:
• By convention, the factorial of 0 is defined to be 1:Copy code0! = 1
3. Factorial of 1:
• The factorial of 1 is also 1: 1! = 1
4. Factorial of a Negative Integer:
• Factorials are not defined for negative integers. The factorial function is only defined for non-negative integers (including zero).
5. Factorial Recursion:
• Factorials can be expressed recursively as follows: n! = n × (n - 1)!
6. Factorial Properties:
• Factorials have several properties, including:
• Multiplying a factorial by a positive integer “k” results in a new factorial: (k × n)! = k! × n!
• Dividing a factorial by a positive integer “k” results in a new factorial: (n / k)! = n! / (n - k)!
• Factorials grow rapidly with increasing “n.” For large values of “n,” the approximation n! ≈ √(2πn) * (n/e)^n is used.

## Applications of Factorial Calculator in Various Fields

A Factorial Calculator, which computes the factorial of a non-negative integer, has various applications in different fields of mathematics, science, engineering, and computer science. Here are some of the key applications of a Factorial Calculator in various fields:

1. Combinatorics:
• Factorials are fundamental in combinatorial mathematics, where they are used to calculate permutations and combinations. They help determine the number of ways to arrange or choose elements from a set.
2. Probability and Statistics:
• In statistics, factorials are used in calculating probabilities, especially in problems involving permutations and combinations. They play a crucial role in probability distributions like the binomial and Poisson distributions.
3. Mathematical Analysis:
• Factorials appear in series expansions and power series, such as Taylor series and Maclaurin series, used for mathematical analysis and approximation of functions.
4. Calculus:
• Factorials are encountered in calculus, particularly in the derivatives and integrals of functions involving factorials.
5. Engineering:
• Engineers use factorials in problems related to reliability analysis, quality control, and system design. They help calculate the probability of success or failure in complex systems.

## Benefits of Using the Factorial Calculator

Here are the key advantages of using such a calculator:

1. Accuracy: Factorial calculations can become complex for large values of “n.” A calculator ensures accurate results without the risk of manual calculation errors.
2. Time-Saving: Factorial calculations can be time-consuming, especially for large numbers. A calculator provides quick results, saving valuable time.
3. Efficiency: It streamlines the process of calculating factorials, making it more efficient, especially when dealing with multiple calculations.
4. Reduced Risk of Errors: Manual calculations of factorials can lead to mistakes, but a calculator minimizes the potential for errors, ensuring reliability.
5. Versatility: Factorial calculators are versatile tools that can handle a wide range of values for “n,” from small integers to very large numbers.

## References

1. “Beyond Repeated Multiplication: Factorials in Combinatorics and Probability” by Discrete Mathematics
2. “From Stirling’s Approximation to Asymptotic Analysis: Unveiling the Hidden Depths of Factorials” by Journal of Mathematical Analysis and Applications

Last Updated : 31 July, 2024

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