Step by Step solution about How to resolve the algorithm Proper divisors step by step in the C# programming language

The given C# code is a program that determines the proper divisors of numbers within a given range (1 to 10) and identifies the number with the highest number of proper divisors within a larger range (1 to 20000).

• ProperDivisors Method:

  • Calculates the proper divisors of a given number. Proper divisors are positive divisors excluding the number itself.
  • It uses the Enumerable.Range and Enumerable.Where methods to generate a sequence of potential divisors and filter out those that divide evenly into the given number.

• Main Method:

  • Iterates through numbers from 1 to 10 and prints their proper divisors.
  • Finds the number between 1 and 20000 with the highest number of proper divisors using LINQ. It creates anonymous objects to store the number and the count of its proper divisors, sorts the list in descending order based on the count, and selects the first item.

• Execution:

  • The program outputs the proper divisors for each number from 1 to 10, separated by commas.
  • Finally, it displays the number with the highest number of proper divisors within the range 1 to 20000.

namespace RosettaCode.ProperDivisors
{
    using System;
    using System.Collections.Generic;
    using System.Linq;

    internal static class Program
    {
        private static IEnumerable<int> ProperDivisors(int number)
        {
            return
                Enumerable.Range(1, number / 2)
                    .Where(divisor => number % divisor == 0);
        }

        private static void Main()
        {
            foreach (var number in Enumerable.Range(1, 10))
            {
                Console.WriteLine("{0}: {{{1}}}", number,
                    string.Join(", ", ProperDivisors(number)));
            }

            var record = Enumerable.Range(1, 20000).Select(number => new
            {
                Number = number,
                Count = ProperDivisors(number).Count()
            }).OrderByDescending(currentRecord => currentRecord.Count).First();
            Console.WriteLine("{0}: {1}", record.Number, record.Count);
        }
    }
}