How to detect whether a given number is Homogeneous or not ?

Homogeneous numbers are not as you describe - two numbers are homogeneous if they have identical prime factors. An example of a homogeneous pair is (6, 72), both of which share prime factors 2 and 3.

Your numbers are palindromes. If you want to work out true homogenoeous numbers, then start with wiki and move to algorithms via Google - but be aware this gets complex, since efficient factorization is the root of most cryptography.

To process palindromic numbers is pretty simple - a non recursive technique is better than a recursive one, it is much easier to work out.

However, since this is your homework, I won't give you any code!

1) Write a method returning a bool, call it IsPalindrome - the method should have a single string parameter
2) Declare an integer, called last, set it to the length of the string, minus one - this is the last character in the string.
3) Set up a loop. A for loop is good, start at zero, end at the string length divided by two, increment by one.
4) In the loop, compare the current character (as given by the loop index) with it's matching character (as given by the last character minus the loop index)
5) If there are different, the string is not a palindrome, so return false immediately.
6) At the end of the loop, the string is a palindrome, so return true.

Done!