The Program in C# Program to Convert Decimal to Octal Number without Array is given below:

using System;

namespace Decimal_to_Octal
{
    class Program
    {
        static void Main(string[] args)
        {
            int decimalNumber, remainder;
            string octalNumber = "";
 Console.WriteLine("Hello Codeauri Family,enter decimal number below to convert it into octal equivalent: ");
            Console.WriteLine("Well,enter a decimal number: ");
            decimalNumber = Convert.ToInt32(Console.ReadLine());

            while (decimalNumber > 0)
            {
                remainder = decimalNumber % 8;
                octalNumber = remainder + octalNumber;
                decimalNumber = decimalNumber / 8;
            }

            Console.WriteLine("Okay, the Octal representation of the decimal number is: " + octalNumber);
            Console.ReadLine();
        }
    }
}

Output:

Hello Codeauri Family,enter decimal number below to convert it into octal equivalent:
Well,enter a decimal number:
10
Okay, the Octal representation of the decimal number is: 12

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Here are the step by step execution of above program:

1. The first line using System; is a directive that tells the compiler to include the System namespace in the program, which is required to use the Convert class.
2. The program has a class named Program that contains the Main method. The Main method is the entry point of the program.
3. In the Main method, two integer variables decimalNumber and remainder are declared to store the decimal number and the remainder obtained after dividing the decimal number by 8, respectively.
4. The octalNumber variable is declared as a string to store the octal representation of the decimal number.
5. The Console.WriteLine method is used to prompt the user to enter a decimal number.
6. The Convert.ToInt32 method is used to convert the input string to an integer and store it in the decimalNumber variable.
7. The while loop is used to convert the decimal number into an octal number. The loop continues until the decimalNumber becomes 0.
8. Inside the loop, the remainder after dividing the decimalNumber by 8 is calculated and stored in the remainder variable.
9. The remainder is concatenated with the octalNumber string to form the octal representation of the decimal number.
10. The decimalNumber is updated by dividing it by 8.
11. The Console.WriteLine method is used to display the octal representation of the decimal number.
12. The Console.ReadLine method is used to wait for the user to press the Enter key before closing the program.