The Amazing Concepts

Kaprekar number is one of the amazing concepts in Mathematics. The square of a number when divided into parts and none of the parts is equal to 0, and sum of both the parts forms the original number, then that number is a Kaprekar number . Let's understand this concept in detail: Checking a Kaprekar Number Following are the steps to check whether any number is a Kaprekar number or not: Step 1 : Consider any number N (must be greater than 0). Step 2 : Square the number N (N x N). Step 3 : Divide the resultant obtained in Step 2 into two parts (left and right). Possible scenarios that occur when dividing the resultant into two parts: Scenario 1 : If the resultant obtained in Step 2 is a single digit number If the resultant obtained in Step 2 is a single digit number (no matter even or odd), compare it with the number considered in Step 1.  If the number in Step 2 is equal to the number in Step 1, it is a Kaprekar number. But if the number  in Step 2 is not equal to the...

D. R. Kaprekar (Dattatreya Ramchandra Kaprekar) introduced an amazing concept Kaprekar number in number theory. Kaprekar number is a natural number whose square when divided into two equal or non-equal parts; left and right, then the sum of both parts must be equal to the original number. None of the parts should have the value zero. The Procedure Step 1: Consider a natural number n. Step 2: Square the number n 2 . Step 3: Divide the value after square into two equal or non-equal parts: left x or x-1 digits and right y digits. Step 4: Add both left and right parts: (x + y) or (x-1 + y). Step 5: If the resultant z is equal to the original number n, then number n is a Kaprekar number, else not. For Example Number n: 9 Square the number n 2 : 9 2 => 81. Divide the value after square into two equal or non-equal parts: 8 and 1. Add both left and right parts: 8 + 1=> 9. Here the resultant 9 is equal to the original number n. Hence, 9 is a Kaprekar number. ...