Dattaraya Ramchandra Kaprekar, born 1905 worked on the number theory. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. Kaprekar discovered the Kaprekar constant or 6174 in 1949. ( tens n n^2 - t) rot /mod over >r + = r> and ; \ If n is a Kaprekar number, return is the power of base for which it \ is Kaprekar. Repeat above three steps until the result of subtraction doesn’t become equal to the previous number. Kaprekar constant. Writing code in comment? He was not respected as he did not have any formal mathematical training. Write Interview
edit 4321 − 1234 = 3087, then 8730 − 0378 = 8352, and In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar’s operation. His claim to fame is the Kaprekar constant 6174. Even mathematicians, till date, aren't sure how to explain this magic number. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,…). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. The set of numbers that converge to zero depends on whether leading zeros are retained (the usual formulation) or are discarded (as in Kaprekar's original formulation). 6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. For example, choose 1495: The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. Kaprekar's constant is equal to 6,174, named after discoverer D. R. Kaprekar. [4] Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. Kaprekar's name today is well-known and many mathematicians have found themselves intrigued by the ideas about numbers which Kaprekar found so addictive. We define the Kaprekar function for base > and power > ,: → to be the following: F p , b ( n ) = α + β {\displaystyle F_{p,b}(n)=\alpha +\beta } , where β = n 2 mod b … 6174 is known as Kaprekar's constant as it was invented by Indian mathematician DR Kaprekar in 1949. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Check the divisibility of Hexadecimal numbers, Count numbers less than N containing digits from the given set : Digit DP, Count of integers of length N and value less than K such that they contain digits only from the given set, Rearrange an array so that arr[i] becomes arr[arr[i]] with O(1) extra space, Rearrange an array such that ‘arr[j]’ becomes ‘i’ if ‘arr[i]’ is ‘j’ | Set 1, Rearrange an array in maximum minimum form | Set 1, Rearrange an array in maximum minimum form | Set 2 (O(1) extra space), Find number of pairs (x, y) in an array such that x^y > y^x, Count smaller elements on right side using Set in C++ STL, Count smaller elements on right side and greater elements on left side using Binary Index Tree, Count inversions in an array | Set 3 (Using BIT), Count Inversions in an array | Set 1 (Using Merge Sort), Fibonacci Heap – Deletion, Extract min and Decrease key, Write a program to print all permutations of a given string, Set in C++ Standard Template Library (STL), https://en.wikipedia.org/wiki/6174_(number), Find Index of given fibonacci number in constant time, Percentage increase in the cylinder if the height is increased by given percentage but radius remains constant, Maximize the first element of the array such that average remains constant, Count numbers from given range having odd digits at odd places and even digits at even places, Modify given array by reducing each element by its next smaller element, Farthest index that can be reached from the Kth index of given array by given operations, Check if given polygon is a convex polygon or not, Split array into equal length subsets with maximum sum of Kth largest element of each subset, Print all possible K-length subsequences of first N natural numbers with sum N, Minimize given flips required to reduce N to 0, Minimize difference between maximum and minimum array elements by exactly K removals, Split squares of first N natural numbers into two sets with minimum absolute difference of their sums, Bakhshali Approximation for computing square roots, Efficient program to print all prime factors of a given number, Program to find GCD or HCF of two numbers, Modulo Operator (%) in C/C++ with Examples. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well … 6174 can be written as the sum of the first three degrees of 18: The sum of squares of the prime factors of 6174 is a square: JAVA executable : run as "java -jar NumberSystemMagic.jar". 6174 is known as Kaprekar’s constant after the Indian mathematician D. R. Kaprekar. Sort four digits in ascending order and store result in a number “asc”. Subtract number larger number from smaller number, i.e., abs(asc – desc). All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. Following is the program to demonstrate the same. Kaprekar Constant 6174 continues to fascinate amateur mathematicians, mathematics teachers and devotees of recreational and experimental mathematics. This article is contributed by Gaurav Saxena. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 6174 is the Kaprekar Constant. Don’t stop learning now. Download JAR : This page was last edited on 20 November 2020, at 17:36. D. R. Kaprekar. : is-kaprekar? : kaprekar ( +n - +n1) dup square >r base @ swap The number 6174 is the first Kaprekar's constant to be discovered, and thus is sometimes known as Kaprekar's constant. Let us look at some of the ideas which he introduced. Kaprekar number is one of those gems, that makes Mathematics fun. Sometimes these numbers (495, 6174, and their counterparts in other digit lengths or in bases other than 10) are called "Kaprekar constants". Attention reader! Take any four-digit number, using at least two different digits (leading zeros are allowed). 6174 is therefore also known as Kaprekar's Constant and this process is known as Kaprekar's Routine. If n is not a Kaprekar number, return zero. How to swap two numbers without using a temporary variable? The mathematician who discovered this curious property in 1949 was Dattathreya Ramchandra Kaprekar or D. R. Kaprekar, a school teacher from Maharashtra with a passion for number theory. Indian recreational mathematician D.R.Kaprekar, found number 6174 – also known as Kaprekar constant – that will return the subtraction result when following this rules: Take any four-digit number, with minimum of two different numbers (1122 or 5151 or 1001 or 4375 and so on.) close, link Let’s try with another number- How about this year as four digit number- 2014 Thus, starting with 1234, we have . See your article appearing on the GeeksforGeeks main page and help other Geeks.