In C programming, what is a simple and common way to check whether a given integer number is a palindrome?

Introduction / Context:
This question checks your understanding of numeric palindromes and basic algorithm design in C. A palindrome is a value that reads the same backward as forward. While palindromes are often discussed for strings, the same idea applies to integers by looking at their decimal digit representation. Knowing a clear, stepwise method to test for palindromes is useful for many coding exercises.

Given Data / Assumptions:

We are dealing with non negative integer values expressed in base 10.
We want a method that can be implemented easily in C using arithmetic operations on integers.
We are not restricted to any specific range of values, as long as they fit into the chosen integer type.

Concept / Approach:
The standard numeric approach is to construct the reverse of the given number by repeatedly extracting its last digit and building a new number. If the reversed number is equal to the original number, then the number is a palindrome. This mirrors the idea of reading the digits from right to left and comparing with the original left to right sequence. There is no direct link between palindromes and prime factors, divisibility tests or sorted digit order.

Step-by-Step Solution:
Store the original value in a variable, for example int n, and keep a copy in original = n. Initialize an integer rev to 0, which will hold the reversed digits. While n is greater than 0, extract the last digit using digit = n % 10 and add it to rev using rev = rev * 10 + digit. Then divide n by 10 to drop the last digit. After the loop ends, rev holds the number formed by reading the digits of original from right to left. Compare original and rev. If they are equal, the number is a palindrome; otherwise, it is not.

Verification / Alternative check:
For example, take n = 121. The loop generates rev = 121, which equals the original number, so 121 is a palindrome. For n = 123, the loop produces rev = 321, which is not equal to 123, so 123 is not a palindrome. This confirms that the reverse and compare method correctly identifies palindromes.

Why Other Options Are Wrong:
Option b about prime factors has no connection to symmetry of digits, so it cannot reliably detect palindromes.
Option c about sorting digits changes the order of digits entirely and cannot preserve the original forward and backward structure required by palindromes.
Option d about divisibility by 11 is only relevant to certain numeric properties and does not characterize all palindromes.

Common Pitfalls:
A common mistake is to forget to keep a copy of the original number before modifying it in the loop, making the final comparison impossible. Another pitfall is mismanaging the loop conditions or using floating point arithmetic unnecessarily. Using integer division and modulo operations keeps the algorithm simple and precise.

Final Answer:
The simplest and most common approach is to reverse the digits of the number using modulo and division, then compare the reversed value to the original to decide whether it is a palindrome.