How to find the "Factorial of an Number" an Algorithm

Factorials are very simple things. They're just products, indicated by an exclamation mark. For instance, "four factorial" is written as "4!" and means 1x2x3x4 = 24. the factorial of any number is that number times the factorial of (1 smaller than that number), factorial(N), for scalar N, is the product of all the integers from 1 to N, i.e. prod(1:n). When N is an N-dimensional array, factorial(N) is the factorial for each element of N.
The factorial function can also be defined for non-integer values using more advanced mathematics. This more generalized definition is used by advanced calculators and mathematical software such as Maple or Mathematica.





Finding Factorial of a given number is another interesting problem. Mathematically represented as n.
For ex:

5! = 5*4*3*2*1.

Not to forget that 1! = 1 and 0! = 1.

We can now generalize the factorial of a given number which is any thing other than zero and one as the product of all the numbers ranging from given number to 1.

i.e n! = n * (n - 1) * (n - 2 ) * ...*1

Algorithm : Factorial

Input : n

Output : Factorial of n

Method
    fact = 1
    for i = n to 1 in steps of -1 do
        fact = fact*i
    end_for
    display 'factorial = ',fact

Algorithm ends

In the above algorithm we have implemented the logic of the equation

n! = n * (n - 1) * (n - 2 ) * ... *1.

The same can be achieved by the following algorithm which follows incremental steps rather than decremental steps of the given algorithm.

Algorithm : Factorial

Input : n

Output : Factorial of n

Method
    fact = 1
    for i = 1 to n in steps of 1 do
        fact = fact*i
    end_for
    display 'factorial = ',fact

Algorithm ends