The Amazing Concepts

The concept of Self number or Devlali number or Colombian number was introduced by D. R. Kaprekar (Dattatreya Ramchandra Kaprekar). Self number or Devlali number or Colombian number is an integer that cannot be expressed as the sum of any other integer and its individual digits. In other words, if any integer y cannot be expressed as the sum of any other integer n and its individual digits, then it is referred to as Self number or Devlali number or Colombian number. Important Points Point 1: All integer n less than 15 give the result less than 20. Point 2: All integer n greater than or equal to 15 give the result greater than 20. The Procedure Step 1: Consider an integer y. Step 2: Take any other integer n. Step 3: Add integer n with its individual digits. Step 4: If the sum is not equal to the original integer y taken in Step 1, then integer y is Self number or Devlali number or Colombian number, else not. For Example Integer y: 20 Take any other integer: 1...

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. ...

The concept of Harshad number was given by D. R. Kaprekar, one of the great mathematicians from the country India. Harshad number or Niven number is any positive integer b that is divisible by its sum of digits (SOD). The term Niven number was coined by Ivan Morton Niven, a Canadian-American mathematician, who specializes in number theory. As per the definition: Harshad number b = number / sum of digits Below are some examples: Number 12 Sum of digits = 1 + 2 => 3 Here, number 12 is divisible by its sum of digits 3, and the resultant is 4. Number 18 Sum of digits = 1 + 8 => 9 Here, number 18 is divisible by its sum of digits 9, and the resultant is 2. Number 72 Sum of digits = 7 + 2 => 9 Here, number 72 is divisible by its sum of digits 9, and the resultant is 8. Number 110 Sum of digits = 1 + 1 + 0 => 2 Here, number 110 is divisible by its sum of digits 2, and the resultant is 55. Number 135 Sum of digits = 1 + 3 + 5 => 9 Here, number...

Dattatreya Ramchandra Kaprekar (D. R. Kaprekar; 1905 – 1986) was an Indian mathematician who discovered several classes of natural numbers including Kaprekar Constant. The number  495  is called Kaprekar Constant for three-digit number. Why is the number 495 called Kaprekar Constant? In 1949, D. R. Kaprekar discovered an interesting property of the number 495 through the mathematical calculations. D. R. Kaprekar observed that when any three-digit number of non-identical digits (not all digits are same) is arranged in two parts – highest number and lowest number, and difference is calculated using subtraction method, then the end-result will be always 495. If the process is continued even after getting the end-result 495, then the end-result will be always 495 at each Iteration, therefore the number 495 is known as Kaprekar Constant. Steps to Follow Take any three-digit number with different digits. Form the highest number and lowest number from this three-digit number. Fi...

Dattatreya Ramchandra Kaprekar (D. R. Kaprekar; 1905 – 1986) was an Indian mathematician who discovered several classes of natural numbers including Kaprekar Constant. The number 6174 is called Kaprekar Constant for four-digit number. Why is the number 6174 called Kaprekar Constant? In 1949, D. R. Kaprekar discovered an interesting property of the number 6174 through the mathematical calculations. D. R. Kaprekar observed that when any four-digit number of non-identical digits (not all digits are same) is arranged in two parts – highest number and lowest number, and difference is calculated using subtraction method, then the end-result will be always 6174 either in the first step or in no more than 7 steps. If the process is continued even after getting the end-result 6174, then the end-result will be always 6174 at each Iteration, therefore the number 6174 is known as Kaprekar Constant. Steps to Follow Take any four-digit number with different digits. Form the highest nu...