**Palindrome**

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

**Palindromic Number**

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

Whether a number is a palindrome or not depends on which base it is represented but all numbers are palindromic in some base.

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**

**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.