Factorial Calculator n!

Calculator Use

Instead of calculating a factorial one digit at a time, use this calculator to calculate the factorial n! of a number n. Enter an integer, up to 5 digits long. You will get the long integer answer and also the scientific notation for large factorials. You may want to copy the long integer answer result and paste it into another document to view it.

Factorial Formula

n! = n × (n - 1) × (n - 2) × (n - 3) × ... × 1

Factorial of 10
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

By definition, the factorial of 0, 0! = 1

What is a Factorial?

A factorial is a function that multiplies a number by every number below it. For example 5!= 5*4*3*2*1=120. The function is used, among other things, to find the number of ways “n” objects can be arranged.

Factorial

There are n! ways of arranging n distinct objects into an ordered sequence.

n

the set or population

In mathematics, there are n! ways to arrange n objects in sequence. "The factorial n! gives the number of ways in which n objects can be permuted."[1] For example:

• 2 factorial is 2! = 2 x 1 = 2
  -- There are 2 different ways to arrange the numbers 1 through 2. {1,2,} and {2,1}.
• 4 factorial is 4! = 4 x 3 x 2 x 1 = 24
  -- There are 24 different ways to arrange the numbers 1 through 4. {1,2,3,4}, {2,1,3,4}, {2,3,1,4}, {2,3,4,1}, {1,3,2,4}, etc.
• 5 factorial is 5! = 5 x 4 x 3 x 2 x 1 = 120
• 0 factorial is a definition: 0! = 1. There is exactly 1 way to arrange 0 objects.

Factorial Problem 1

How many different ways can the letters in the word “document” be arranged?

For this problem we simply take the number of letters in the word and find the factorial of that number. This works because each letter in the word is unique and we are simply finding the maximum amount of ways 8 items can be ordered.

8!=8*7*6*5*4*3*2*1= 40,320

Factorial Problem 2

How many different ways can the letters in the word “physics” be arranged?

This problem is slightly different because there are two “s” letters. To account for this we divide by the number of duplicate letters factorial. There are 7 letters in the word physics and two duplicate letters so we must find 7!/2!. If the word had multiple duplicates, as in “little,” the formula would be 6!/(2! * 2!).

7!/2!=(7*6*5*4*3*2*1)/(2*1)= 2,520

References

[1] For more information on factorials please see the Factorial page at Wolfram MathWorld.

See also the Multifactorial Calculator to compute n! to n!!!!!