# Palindromic divisors of a number

Prerequiste: Find all divisors of a natural number
Given a number N. The task is to find all the palindromic divisors of N.

Examples:

Input: N = 66
Output: 1 2 3 6 11 22 33 66

Input: N = 808
Output: 1 2 4 8 101 202 404 808

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Find all the divisors of N using approach discussed in this article.
• For each divisors D, check whether D is palindromic or not.
• Repeat the above step for all the divisors.

Below is the implementation of the above approach:

## C++

 `// C++ program to find all the palindromic ` `// divisors of a number ` `#include "bits/stdc++.h" ` `using` `namespace` `std; ` ` `  `// Function to check is num is palindromic ` `// or not ` `bool` `isPalindrome(``int` `n) ` `{ ` `    ``// Convert n to string str ` `    ``string str = to_string(n); ` ` `  `    ``// Starting and ending index of ` `    ``// string str ` `    ``int` `s = 0, e = str.length() - 1; ` `    ``while` `(s < e) { ` ` `  `        ``// If char at s and e are ` `        ``// not equals then return ` `        ``// false ` `        ``if` `(str[s] != str[e]) { ` `            ``return` `false``; ` `        ``} ` `        ``s++; ` `        ``e--; ` `    ``} ` `    ``return` `true``; ` `} ` ` `  `// Function to find  palindromic divisors ` `void` `palindromicDivisors(``int` `n) ` `{ ` `    ``// To sore the palindromic divisors of ` `    ``// number n ` `    ``vector<``int``> PalindromDivisors; ` ` `  `    ``for` `(``int` `i = 1; i <= ``sqrt``(n); i++) { ` ` `  `        ``// If n is divisible by i ` `        ``if` `(n % i == 0) { ` ` `  `            ``// Check if number is a perfect square ` `            ``if` `(n / i == i) { ` ` `  `                ``// Check divisor is palindromic, ` `                ``// then store it ` `                ``if` `(isPalindrome(i)) { ` `                    ``PalindromDivisors.push_back(i); ` `                ``} ` `            ``} ` `            ``else` `{ ` ` `  `                ``// Check if divisors are palindrome ` `                ``if` `(isPalindrome(i)) { ` `                    ``PalindromDivisors.push_back(i); ` `                ``} ` ` `  `                ``// Check if n / divisors is palindromic ` `                ``// or not ` `                ``if` `(isPalindrome(n / i)) { ` `                    ``PalindromDivisors.push_back(n / i); ` `                ``} ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Print all palindromic divisors in sorted order ` `    ``sort(PalindromDivisors.begin(), ` `         ``PalindromDivisors.end()); ` ` `  `    ``for` `(``int` `i = 0; i < PalindromDivisors.size(); ` `         ``i++) { ` `        ``cout << PalindromDivisors[i] << ``" "``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 66; ` ` `  `    ``// Function call to find all palindromic ` `    ``// divisors ` `    ``palindromicDivisors(n); ` `} `

## Java

 `// Java program to find all the palindromic ` `// divisors of a number ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to check is num is palindromic ` `// or not ` `static` `boolean` `isPalindrome(``int` `n) ` `{ ` `    ``// Convert n to String str ` `    ``String str = String.valueOf(n); ` ` `  `    ``// Starting and ending index of ` `    ``// String str ` `    ``int` `s = ``0``, e = str.length() - ``1``; ` `    ``while` `(s < e) { ` ` `  `        ``// If char at s and e are ` `        ``// not equals then return ` `        ``// false ` `        ``if` `(str.charAt(s) != str.charAt(e)) { ` `            ``return` `false``; ` `        ``} ` `        ``s++; ` `        ``e--; ` `    ``} ` `    ``return` `true``; ` `} ` ` `  `// Function to find palindromic divisors ` `static` `void` `palindromicDivisors(``int` `n) ` `{ ` `    ``// To sore the palindromic divisors of ` `    ``// number n ` `    ``Vector PalindromDivisors = ``new` `Vector(); ` ` `  `    ``for` `(``int` `i = ``1``; i <= Math.sqrt(n); i++) { ` ` `  `        ``// If n is divisible by i ` `        ``if` `(n % i == ``0``) { ` ` `  `            ``// Check if number is a perfect square ` `            ``if` `(n / i == i) { ` ` `  `                ``// Check divisor is palindromic, ` `                ``// then store it ` `                ``if` `(isPalindrome(i)) { ` `                    ``PalindromDivisors.add(i); ` `                ``} ` `            ``} ` `            ``else` `{ ` ` `  `                ``// Check if divisors are palindrome ` `                ``if` `(isPalindrome(i)) { ` `                    ``PalindromDivisors.add(i); ` `                ``} ` ` `  `                ``// Check if n / divisors is palindromic ` `                ``// or not ` `                ``if` `(isPalindrome(n / i)) { ` `                    ``PalindromDivisors.add(n / i); ` `                ``} ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Print all palindromic divisors in sorted order ` `    ``Collections.sort(PalindromDivisors); ` ` `  `    ``for` `(``int` `i = ``0``; i < PalindromDivisors.size(); ` `        ``i++) { ` `        ``System.out.print(PalindromDivisors.get(i)+ ``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``66``; ` ` `  `    ``// Function call to find all palindromic ` `    ``// divisors ` `    ``palindromicDivisors(n); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 program to find all the palindromic  ` `# divisors of a number ` `from` `math ``import` `sqrt; ` ` `  `# Function to check is num is palindromic  ` `# or not  ` `def` `isPalindrome(n) :  ` ` `  `    ``# Convert n to string str  ` `    ``string ``=` `str``(n);  ` ` `  `    ``# Starting and ending index of  ` `    ``# string str  ` `    ``s ``=` `0``; e ``=` `len``(string) ``-` `1``;  ` `    ``while` `(s < e) : ` ` `  `        ``# If char at s and e are  ` `        ``# not equals then return  ` `        ``# false  ` `        ``if` `(string[s] !``=` `string[e]) : ` `            ``return` `False``;  ` `         `  `        ``s ``+``=` `1``;  ` `        ``e ``-``=` `1``;  ` `     `  `    ``return` `True``;  ` ` `  `# Function to find palindromic divisors  ` `def` `palindromicDivisors(n) :  ` ` `  `    ``# To sore the palindromic divisors of  ` `    ``# number n  ` `    ``PalindromDivisors ``=` `[];  ` ` `  `    ``for` `i ``in` `range``(``1``, ``int``(sqrt(n))) : ` ` `  `        ``# If n is divisible by i  ` `        ``if` `(n ``%` `i ``=``=` `0``) : ` ` `  `            ``# Check if number is a perfect square  ` `            ``if` `(n ``/``/` `i ``=``=` `i) : ` ` `  `                ``# Check divisor is palindromic,  ` `                ``# then store it  ` `                ``if` `(isPalindrome(i)) : ` `                    ``PalindromDivisors.append(i);  ` `             `  `            ``else` `: ` ` `  `                ``# Check if divisors are palindrome  ` `                ``if` `(isPalindrome(i)) : ` `                    ``PalindromDivisors.append(i);  ` ` `  `                ``# Check if n / divisors is palindromic  ` `                ``# or not  ` `                ``if` `(isPalindrome(n ``/``/` `i)) : ` `                    ``PalindromDivisors.append(n ``/``/` `i);  ` ` `  `    ``# Print all palindromic divisors in sorted order  ` `    ``PalindromDivisors.sort();  ` `     `  `    ``for` `i ``in` `range``(``len``( PalindromDivisors)) : ` `        ``print``(PalindromDivisors[i] ,end``=``" "``);  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``n ``=` `66``;  ` ` `  `    ``# Function call to find all palindromic  ` `    ``# divisors  ` `    ``palindromicDivisors(n);  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# program to find all the palindromic ` `// divisors of a number ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to check is num is palindromic ` `// or not ` `static` `bool` `isPalindrome(``int` `n) ` `{ ` `    ``// Convert n to String str ` `    ``String str = String.Join(``""``,n); ` ` `  `    ``// Starting and ending index of ` `    ``// String str ` `    ``int` `s = 0, e = str.Length - 1; ` `    ``while` `(s < e) ` `    ``{ ` ` `  `        ``// If char at s and e are ` `        ``// not equals then return ` `        ``// false ` `        ``if` `(str[s] != str[e]) ` `        ``{ ` `            ``return` `false``; ` `        ``} ` `        ``s++; ` `        ``e--; ` `    ``} ` `    ``return` `true``; ` `} ` ` `  `// Function to find palindromic divisors ` `static` `void` `palindromicDivisors(``int` `n) ` `{ ` `    ``// To sore the palindromic divisors of ` `    ``// number n ` `    ``List<``int``> PalindromDivisors = ``new` `List<``int``>(); ` ` `  `    ``for` `(``int` `i = 1; i <= Math.Sqrt(n); i++)  ` `    ``{ ` ` `  `        ``// If n is divisible by i ` `        ``if` `(n % i == 0)  ` `        ``{ ` ` `  `            ``// Check if number is a perfect square ` `            ``if` `(n / i == i) ` `            ``{ ` ` `  `                ``// Check divisor is palindromic, ` `                ``// then store it ` `                ``if` `(isPalindrome(i)) ` `                ``{ ` `                    ``PalindromDivisors.Add(i); ` `                ``} ` `            ``} ` `            ``else` `            ``{ ` ` `  `                ``// Check if divisors are palindrome ` `                ``if` `(isPalindrome(i)) ` `                ``{ ` `                    ``PalindromDivisors.Add(i); ` `                ``} ` ` `  `                ``// Check if n / divisors is palindromic ` `                ``// or not ` `                ``if` `(isPalindrome(n / i))  ` `                ``{ ` `                    ``PalindromDivisors.Add(n / i); ` `                ``} ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Print all palindromic divisors in sorted order ` `    ``PalindromDivisors.Sort(); ` ` `  `    ``for` `(``int` `i = 0; i < PalindromDivisors.Count; ` `        ``i++)  ` `    ``{ ` `        ``Console.Write(PalindromDivisors[i]+ ``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `n = 66; ` ` `  `    ``// Function call to find all palindromic ` `    ``// divisors ` `    ``palindromicDivisors(n); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

Output:

```1 2 3 6 11 22 33 66
```

Time Complexity: O(N*log N)

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