A Palindrome Number is a number that remains the same when its digits are reversed. For example, 121 and 12321 are palindrome numbers, while 123 and 456 are not.

Logic to Check if a Number is Palindrome:

1. Reverse the number using the same method as reversing a number.
2. Compare the reversed number with the original number.
3. If they are the same, the number is a palindrome; otherwise, it is not.

Program:

Here’s a simple C program to check whether a number is a palindrome:

#include <stdio.h>

int main() {
    int num, reversed = 0, remainder, original;

    // Input a number from the user
    printf("Enter an integer: ");
    scanf("%d", &num);

    original = num; // Store the original number

    // While loop to reverse the digits of the number
    while (num != 0) {
        remainder = num % 10;               // Extract the last digit
        reversed = reversed * 10 + remainder;  // Build the reversed number
        num = num / 10;                     // Remove the last digit from the original number
    }

    // Check if the original number and the reversed number are the same
    if (original == reversed) {
        printf("%d is a palindrome.\n", original);
    } else {
        printf("%d is not a palindrome.\n", original);
    }

    return 0;
}

Explanation:

1. Variables:

   • int num: This variable holds the number input by the user.
   • int reversed: This variable will store the reversed number, initialized to 0.
   • int remainder: This variable is used to store the last digit of the original number.
   • int original: This variable stores the original number to compare later.

2. Input:

   • The user is prompted to enter a number, which is stored in num.

3. Reversing Logic:

   • The program enters a while loop that runs until num is not equal to 0.
   • Inside the loop:
     • remainder = num % 10; extracts the last digit of num.
     • reversed = reversed * 10 + remainder; builds the reversed number.
     • num = num / 10; removes the last digit from num.

4. Comparison:

   • After the loop, the program checks if the original number (original) is equal to the reversed number (reversed).
   • If they are equal, the number is a palindrome, and the program prints that it is a palindrome. Otherwise, it prints that it is not a palindrome.

Sample Output:

Example 1:

Enter an integer: 121
121 is a palindrome.

Example 2:

Enter an integer: 12345
12345 is not a palindrome.

Key Points:

• Reversing Logic: The same technique is used to reverse the number as in the previous example.
• Comparison: The program compares the reversed number with the original number to determine if it is a palindrome.
• This program effectively demonstrates basic C concepts, including loops, conditionals, and arithmetic operations.