Factorial Calculator Online Free Tool

Factorial Calculator

 

Factorial Calculator: Compute Factorials Quickly and Easily

Calculating a factorial one digit at a time can be tedious. Instead, use our factorial calculator to compute the factorial $n!$ of any number $n$ efficiently. Enter an integer (up to 5 digits long) to get both the long integer result and, if applicable, the scientific notation for large factorials. You can copy the long integer result and paste it into another document for a detailed view.

What is a Factorial?

A factorial, denoted as $n!$, is a mathematical function that multiplies a number by every number below it. For example:

$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

Factorials are used in various mathematical contexts, including permutations and combinations, to determine the number of possible arrangements of $n$ distinct objects.

 

Factorial Formula:

$n! = n \times (n - 1) \times (n - 2) \times \cdots \times 1$

Examples of Factorials

• Factorial of 10:
  

  $10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800$

• Factorial of 0:
  

  By definition, $0! = 1$

Why Use Our Factorial Calculator?

Our factorial calculator simplifies the process of computing factorials, especially for large numbers. Benefits include:

• Accuracy: Provides precise results for both long integer answers and scientific notation.
• Convenience: Quickly compute factorials without manual calculations.
• Versatility: Suitable for a range of applications, from mathematical problems to statistical analyses.

Understanding Factorials in Permutations

Factorials are essential in combinatorics to determine the number of ways $n$ objects can be arranged. For example:

• 2 Factorial:
  

  $2! = 2 \times 1 = 2$
  There are 2 different ways to arrange the numbers 1 and 2: {1,2} and {2,1}.

• 4 Factorial:
  

  $4! = 4 \times 3 \times 2 \times 1 = 24$
  There are 24 different ways to arrange the numbers 1 through 4.

• 5 Factorial:
  

  $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

Factorial Problems

Problem 1: Arrange the Letters in "Document"

To determine how many different ways the letters in the word "document" can be arranged, calculate:

$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320$

Problem 2: Arrange the Letters in "Physics"

For words with duplicate letters, divide by the factorial of the number of duplicate letters. For "physics":

$\frac{7!}{2!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 2,520$

If there are multiple duplicates, such as in “little,” use the formula:

$\frac{6!}{2! \times 2!}$

References:

For additional information on factorials, visit the Factorial page at Wolfram MathWorld.

Try the Online Free Factorial Calculator now!