Palindromic Numbers or Palindromes

Palindrome

A palindrome is one that is the same when the digits are reversed.

Every family has a palindrome in it such as MUM and DAD, since a palindrome is a word that is the same when reversed. Perhaps your name is a palindrome, for example, EVE, BOB, ANNA etc.

Palindromic Number

A palindromic number is a number which remains the same even if its digits are reversed. 

For example 28582. All numbers turn out to be palindromes in some number base.

We can have palindromic numbers also, for example, 49194.
Whether a number is a palindrome or not depends on which base it is represented but all numbers are palindromic in some base.

Numbers that read the same backwards and forwards.

The number "17371" is a palindromic number.

"5" is also a palindromic number.

But "2345" is NOT, because backwards it is "5432" (not the same).

Some More Examples of Palindromic Numbers

1. Square of 11, i.e. 121 is a palindromic number.

2. Square of 111, i.e. 12321 is a palindromic number.

3. Square of 1111, i.e. 1234321 is a palindromic number.

4. Cube of 11, i.e. 1331 is a palindromic number.

5. Cube of 111, i.e. 1367631 is a palindromic number.

How to Find a Palindromic Number Using a Given Number

Using a given number, we can find a palindromic number using the following steps.

Step 1: Start with any number. Call it original number. Reverse the digits of the original number.

Step 2: Call the reversed number as new number. Add the new number to the original number.

Step 3: If the sum is a palindrome, you are done. If the sum is not a palindrome, repeat the steps 1 and 2 taking this sum as original number.

Example 1: Find a palindromic number by taking 754 as original number.

Solution:

Step 1: The original number is 754. Reverse the digits of 754.
Reversing 754 gives 457.

Step 2: Adding 754 and 457 gives 1211.

Step 3: 1211 is not a palindrome, so repeat the steps 1 and 2.

Repeating steps 1 and 2, we get,

Step 1: Take 1211 as original number. Reverse the digits of 1211.
Reversing 1211 gives 1121.

Step 2: Add 1211 to 1121.
After adding 1211 and 1121, we get 2332.

Step 3: We are done since 2332 can read the same backward and forward!

Hence, 2332 is a palindromic number.

Brief Steps to Find the Palindromic Numbers