The value of zero factorial is 1. The factorial of any number "n" is calculated by multiplying all the numbers between n and 1 (including n). So one might ask what is the value of zero factorial; the value of 0! is 1, and this is calculated using various methods.
Factorial
The Factorial of any number is calculated by finding the product of n and all numbers less than n, till it reaches 1. Another definition of factorial can be defined as the factorial of a whole number is the function that multiplies the number by every natural number less than it. The factorial of any number is represented by denoting an exclamation mark after it, symbolically it is written as n!. Factorials are used to calculate permutation and combination.
Factorial of a number can be calculated in several ways. For example, if we have to calculate the factorial of 5, then it can be represented s 5! = 5 × 4 × 3 × 2 × 1 = 120. So, the value of 5! = 120.
Why is Factorial of 0 is always 1?
The value of Zero factorial is equal to 1. Symbolically, it can be represented as 0! = 1. We can prove that the value of zero factorial is equal to 1 in different ways. As factorial is used to calculate the permutation and combination of any number, logically the meaning of zero factorial is to arrange data that contains no value. So, the way of arranging any data which contains no values is in only one way. So the value of 0! is equal to 1.
0! = 1
Zero Factorial Explained
The value of 0! factorial is equal to 1. Let's see how we can derive it using the above formula for calculating factorial:
We can write, n! = (n+1)!/(n+1)
0! = (0 + 1)!/(0 + 1)
⇒ 0! = (1)!/(1)
⇒ 0! = 1/1
⇒ 0! = 1
Thus, the factorial of 0 is one.
Derivation of Zero Factorial is Equal to 1
The formula for calculating the factorial of any number is equal to the product of all the positive numbers less than or equal to a number.
Formula for n! = n × (n-1) × (n-2) × (n-3) × (n-4)........ × 1
Above formula can also be written as n! = n × (n-1)!
For the value of 1! = 1 × (1-1)!
1! = 1 × 0!
The value of LHS should always be equal to the value of RHS
For LHS = RHS, a value of 0! must be equal to 1
Hence, 0! = 1