Kaprekar Constant

6174 is the Kaprekar Constant. This number is special as we always get this number when following steps are followed for any four digit number such that all digits of number are not same, i.e., all four digit numbers excluding (0000, 1111, …)

  1. Sort four digits in ascending order and store result in a number “asc”.
  2. Sort four digits in descending order and store result in a number “desc”.
  3. Subtract number larger number from smaller number, i.e., abs(asc – desc).
  4. Repeat above three steps until the result of subtraction doesn’t become equal to the previous number.

We always end up with 6174.

Following is the program to demonstrate the same.

C++



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// C++ program to demonstrate working of
// Kaprekar constant
#include<bits/stdc++.h>
using namespace std;
  
// This function checks validity of kaprekar's
// constant. It returns kaprekar's constant for
// any four digit number "n" such that all digits
// of n are not same.
int kaprekarRec(int n, int &prev)
{
    if (n == 0)
       return 0;
  
    // Store current n as previous number
    prev = n;
  
    // Get four digits of given number
    int digits[4];
    for (int i=0; i<4; i++)
    {
       digits[i] = n%10;
       n = n/10;
    }
  
    // Sort all four dgits in ascending order
    // And giet in the form of number "asc"
    sort(digits, digits+4);
    int asc = 0;
    for (int i=0; i<4; i++)
       asc = asc*10 + digits[i];
  
    // Get all four dgits in descending order
    // in the form of number "desc"
    sort(digits, digits+4, std::greater<int> ());
    int desc = 0;
    for (int i=0; i<4; i++)
       desc = desc*10 + digits[i];
  
    // Get the difference of two numbers
    int diff = abs(asc - desc);
  
    // If difference is same as previous, we have
    // reached kaprekar's constant
    if (diff == prev)
        return diff;
  
    // Else recur
    return kaprekarRec(diff, prev);
}
  
// A wrapper over kaprekarRec()
int kaprekar(int n)
{
    int prev = 0;
    return kaprekarRec(n, prev);
}
  
// Driver code
int main()
{
    // Trying few four digit numbers, we
    // always get 6174
    cout << kaprekar(1000) << endl;
    cout << kaprekar(1112) << endl;
    cout << kaprekar(9812) << endl;
    return 0;
}

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Java

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// Java program to demonstrate working of 
// Kaprekar constant 
import java.util.Arrays;
  
class GFG{
// This function checks validity of kaprekar's 
// constant. It returns kaprekar's constant for 
// any four digit number "n" such that all digits 
// of n are not same. 
static int kaprekarRec(int n, int prev) 
    if (n == 0
    return 0
  
    // Store current n as previous number 
    prev = n; 
  
    // Get four digits of given number 
    int[] digits=new int[4]; 
    for (int i=0; i<4; i++) 
    
    digits[i] = n%10
    n = n/10
    
  
    // Sort all four dgits in ascending order 
    // And giet in the form of number "asc" 
    Arrays.sort(digits);
    int asc = 0
    for (int i=0; i<4; i++) 
    asc = asc*10 + digits[i]; 
  
    // Get all four dgits in descending order 
    // in the form of number "desc" 
    Arrays.sort(digits); 
    int desc = 0
    for (int i=3; i>=0; i--) 
    desc = desc*10 + digits[i]; 
  
    // Get the difference of two numbers 
    int diff = Math.abs(asc - desc); 
  
    // If difference is same as previous, we have 
    // reached kaprekar's constant 
    if (diff == prev) 
        return diff; 
  
    // Else recur 
    return kaprekarRec(diff, prev); 
  
// A wrapper over kaprekarRec() 
static int kaprekar(int n) 
    int prev = 0
    return kaprekarRec(n, prev); 
  
// Driver code 
public static void main(String[] args) 
    // Trying few four digit numbers, we 
    // always get 6174 
    System.out.println(kaprekar(1000)); 
    System.out.println(kaprekar(1112)); 
    System.out.println(kaprekar(9812)); 
}
// This code is contributed by mits

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Python3

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# Python3 program to demonstrate 
# working of Kaprekar constant 
  
# This function checks validity of
# kaprekar's constant. It returns 
# kaprekar's constant for any four 
# digit number "n" such that all 
# digits of n are not same. 
def kaprekarRec(n, prev): 
  
    if (n == 0):
        return 0
  
    # Store current n as previous 
    # number 
    prev = n; 
  
    # Get four digits of given number 
    digits = [0] * 4
    for i in range(4):
        digits[i] = n % 10;
        n = int(n / 10); 
  
    # Sort all four dgits in ascending order 
    # And giet in the form of number "asc" 
    digits.sort(); 
    asc = 0
    for i in range(4):
        asc = asc * 10 + digits[i]; 
  
    # Get all four dgits in descending order 
    # in the form of number "desc" 
    digits.sort(); 
    desc = 0
    for i in range(3, -1, -1):
        desc = desc * 10 + digits[i]; 
  
    # Get the difference of two numbers 
    diff = abs(asc - desc); 
  
    # If difference is same as previous, 
    # we have reached kaprekar's constant 
    if (diff == prev): 
        return diff; 
  
    # Else recur 
    return kaprekarRec(diff, prev); 
  
# A wrapper over kaprekarRec() 
def kaprekar(n): 
  
    rev = 0
    return kaprekarRec(n, rev); 
  
# Driver code 
  
# Trying few four digit numbers,  
# we always get 6174 
print(kaprekar(1000)); 
print(kaprekar(1112)); 
print(kaprekar(9812));
  
# This code is contributed by mits.

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C#

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// C# program to demonstrate working of 
// Kaprekar constant 
using System;
  
class GFG{
// This function checks validity of kaprekar's 
// constant. It returns kaprekar's constant for 
// any four digit number "n" such that all digits 
// of n are not same. 
static int kaprekarRec(int n, int prev) 
    if (n == 0) 
    return 0; 
  
    // Store current n as previous number 
    prev = n; 
  
    // Get four digits of given number 
    int[] digits=new int[4]; 
    for (int i=0; i<4; i++) 
    
    digits[i] = n%10; 
    n = n/10; 
    
  
    // Sort all four dgits in ascending order 
    // And giet in the form of number "asc" 
    Array.Sort(digits);
    int asc = 0; 
    for (int i=0; i<4; i++) 
    asc = asc*10 + digits[i]; 
  
    // Get all four dgits in descending order 
    // in the form of number "desc" 
    Array.Sort(digits); 
    int desc = 0; 
    for (int i=3; i>=0; i--) 
    desc = desc*10 + digits[i]; 
  
    // Get the difference of two numbers 
    int diff = Math.Abs(asc - desc); 
  
    // If difference is same as previous, we have 
    // reached kaprekar's constant 
    if (diff == prev) 
        return diff; 
  
    // Else recur 
    return kaprekarRec(diff, prev); 
  
// A wrapper over kaprekarRec() 
static int kaprekar(int n) 
    int prev = 0; 
    return kaprekarRec(n, prev); 
  
// Driver code 
public static void Main() 
    // Trying few four digit numbers, we 
    // always get 6174 
    System.Console.WriteLine(kaprekar(1000)); 
    System.Console.WriteLine(kaprekar(1112)); 
    System.Console.WriteLine(kaprekar(9812)); 
}
// This code is contributed by mits

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PHP

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<?php
// PHP program to demonstrate working of 
// Kaprekar constant 
  
// This function checks validity of kaprekar's 
// constant. It returns kaprekar's constant 
// for any four digit number "n" such that 
// all digits of n are not same. 
function kaprekarRec($n, $prev
    if ($n == 0) 
    return 0; 
  
    // Store current n as previous number 
    $prev = $n
  
    // Get four digits of given number 
    $digits = array_fill(0, 4, 0); 
    for ($i = 0; $i < 4; $i++) 
    
        $digits[$i] = $n % 10; 
        $n = (int)($n / 10); 
    
  
    // Sort all four dgits in ascending order 
    // And giet in the form of number "asc" 
    sort($digits); 
    $asc = 0; 
    for ($i = 0; $i < 4; $i++) 
    $asc = $asc * 10 + $digits[$i]; 
  
    // Get all four dgits in descending order 
    // in the form of number "desc" 
    rsort($digits); 
    $desc = 0; 
    for ($i = 0; $i < 4; $i++) 
    $desc = $desc * 10 + $digits[$i]; 
  
    // Get the difference of two numbers 
    $diff = abs($asc - $desc); 
  
    // If difference is same as previous, 
    // we have reached kaprekar's constant 
    if ($diff == $prev
        return $diff
  
    // Else recur 
    return kaprekarRec($diff, $prev); 
  
// A wrapper over kaprekarRec() 
function kaprekar($n
    $rev = 0; 
    return kaprekarRec($n, $rev); 
  
// Driver code 
  
// Trying few four digit numbers, we 
// always get 6174 
echo kaprekar(1000) . "\n"
echo kaprekar(1112) . "\n"
echo kaprekar(9812) . "\n";
  
// This code is contributed by mits.
?>

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Output :

6174
6174
6174

Illustration :

n = 2324
1) asc  = 2234
2) desc = 4322
3) Difference = 2088 
4) Repeating above steps as difference is not same
as n

n = 2088
1) asc  = 0288
2) desc = 8820
3) Difference = 8532  
4) Repeating above steps as difference is not same
as n.

n = 8532
1) asc  = 2358
2) desc = 8532
3) Difference = 6174  
4) Repeating above steps as difference is not same
as n.

n = 6174
1) asc  = 1467
2) desc = 7641
3) Difference = 6174  
Stopping here as difference is same as n.

Reference:
https://en.wikipedia.org/wiki/6174_(number)

Related Article:
Kaprekar Number

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