Theoretical - Inverse Factorial

In mathematics, the factorial of a integer n, denoted by n!, is the product of all positive integers less than or equal to n.

Practical - Inverse Factorial

Write a function that returns a number if its factorial is given. If the input value does not have a solution, return 0.

Example:

input         : 120
output        : 5

We create a loop counting from one to infinite. And in every loop we check that if number can be divided without remainder and multiply the products until we reach to input value.

Here is a solution using Python.

def inverse_fact(input):
    prod = 1
    i = 1
    while True:
        if input % i == 0: # If divided without remainder
            prod *= i
            if prod == input:
                return i
        else:
            return 0
        i += 1

Here is a solution using MATLAB.

function output = reverse_fact(input)
% Inverse Factorial Function
    prod = 1;
    i = 1;
    while(true)
        if(mod(input, i) == 0) % If divided without remainder
            prod = prod * i;
            if(prod == input)
                break; % Exit loop
            end
        else
            i = 0;
            break;
        end
        i = i + 1;
    end
    output = i;
end