Write a Python program that displays a prompt to the user requesting the input of two integer numbers. After the user inputs the two numbers, the program should calculate and output the greatest common divisor (GCD) of the two numbers. The program should use a function to calculate the GCD value and display the result in the console. The function should have a clear name describing what it does and be well-documented using comments. The program should also handle cases where at least one of the input numbers is negative or zero. Finally, the program should be tested with various input combinations to ensure that it works as expected.
This prompt doesn't seem malicious.