Factorial Calculator

A factorial calculator is a mathematical tool that computes the factorial of a given positive integer. The factorial of a number n (denoted as n!) is the product of all positive integers from 1 to n. This tool is essential for students, mathematicians, and professionals working with permutations, combinations, and probability calculations.

What is a Factorial?

In mathematics, a factorial is a function that represents the product of all positive integers from 1 to a given non-negative integer. It is typically denoted by an exclamation mark (!) after a number.

How to calculate Factorial?

To calculate the factorial manually, you need to follow these steps:

1. Choose the number for which you want to calculate the factorial; let's call it n.
2. Start from 1 and create a list of numbers from 1 to n.
3. Based on this list of numbers, perform consecutive multiplications from 1 to n. This means you start with 1 and multiply it by 2, then continue multiplying by 3, 4, and so on until you multiply by n.
4. Once you have multiplied all the numbers from 1 to n, the result of this multiplication is the factorial of n.
5. Record this result or use it for your intended purpose.

The Factorial formula:

n! = n × (n-1) × (n-2) × ... × 2 × 1

Example

For example, to calculate 5!, you would do the following:

5! = 5 × 4 × 3 × 2 × 1 = 120

So, 5! = 120.

If you want to calculate the factorial of a different number, simply replace n with that number in the calculation.

Special cases:

• 0! = 1 (by definition)
• 1! = 1
• Factorials grow very rapidly: 10! = 3,628,800

Applications of Factorials:

• Permutations: Arrangements of objects in a specific order
• Combinations: Selections of objects without regard to order
• Probability calculations
• Taylor series expansions
• Stirling's approximation for large factorials