The Number 1089: A Magical Number

The number 1089 is considered a magical number as far as the number theory is concerned. Why is this number considered a magical number? The answer to this question is described in this post.

The Concept

Step 1: Take any three-digit positive integer with non-identical digits (not all digits are same).

Step 2: Reverse the digits of the number to form mirror number

Step 3: Subtract mirror number from the original number taken in Step 1.

Step 4: Calculate the difference and reverse the digits of the difference.

Step 5: Add the digits of the difference to its reverse digits. The end-result is always the number 1089.

For Example

Number 123

Mirror number formed after reversing the digits is 321.

Subtract mirror number from the original number: 123 – 321 => -(198).

Difference after calculation is 198 and its reverse digits are 891.

Adding digits of the difference to its reverse digits: [198 + 891] => 1089.

As you can see, the end-result is the number 1089.

Number 456

Mirror number formed after reversing the digits is 654.

Subtract mirror number from the original number: 456 – 654 => -(198).

Difference after calculation is 198 and its reverse digits are 891.

Adding digits of the difference to its reverse digits: [198 + 891] => 1089.

As you can see, the end-result is the number 1089.

Number 789

Mirror number formed after reversing the digits is 987.

Subtract mirror number from the original number: 789 – 987 => -(198).

Difference after calculation is 198 and its reverse digits are 891.

Adding digits of the difference to its reverse digits: [198 + 891] => 1089.

As you can see, the end-result is the number 1089.

Hope you have understood this amazing concept of the number 1089. You can try yourself using any other three-digit number. In case of any issue, kindly provide your valuable comments.