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# Kaprekar Number

A Kaprekar number is a non-negative integer whose square, when divided into two parts, such that the sum of the parts is equal to the original number. The two parts can have leading zeros.

For example, 45 is a Kaprekar number because:

45² = 2025 20 + 25 = 45

Similarly, 297 is a Kaprekar number because:

297² = 88209 88 + 209 = 297

The concept of Kaprekar numbers is named after D.R. Kaprekar, an Indian mathematician who discovered the concept in 1949.

Kaprekar numbers have interesting properties, and there are many fascinating patterns to be found within the sequence of Kaprekar numbers.

Test 1 is 95 Kaprekar number?

No, 95 is not a Kaprekar number.

To check if a number is a Kaprekar number, you need to square the number and then split the result into two parts, such that their sum equals the original number. Let's try this for 95:

95² = 9025

To find out if 95 is a Kaprekar number, we need to try splitting 9025 into two parts. We can split it in the following ways:

9 + 025 = 34 (not equal to 95) 90 + 25 = 115 (not equal to 95) 902 + 5 = 907 (not equal to 95) 9025 + 0 = 9025 (not a valid split)

Since none of the possible splits equal 95, we can conclude that 95 is not a Kaprekar number.

Test 2 is 99 Kaprekar ?

Yes, 99 is a Kaprekar number.

99² = 9801, and 98 + 01 = 99.

Therefore, 99 satisfies the definition of a Kaprekar number.

Here given code implementation process.

``````//C Program
//Check if a given number is kaprekar number or not
#include <stdio.h>
#include <math.h>

//Count the number of digits in number
int digit_length(int number)
{
int size = 0;

while (number!=0)
{
number/=10;

size++;
}
return size;
}

// Check whether given number is kaprekar number or not
int is_kaprekar(int number)
{
if (number == 1) {
return 1;
}

// Calculate square of given number
int square = number * number;

// Get the length of digits in given number square
int size = digit_length(square);

int sum = 0;

int parts = 0;

for (int digit = 1; digit < size; ++digit)
{
parts = pow(10, digit);

if (parts != number)
{
// Combine parts of square numbers
sum = ( square / parts ) + ( square % parts );

if (sum == number)
{
//When square digit sum is equal to number
return 1;
}
}
}

return 0;
}

void kaprekar(int number)
{
if(is_kaprekar(number) == 1)
{
//When Yes
printf("%d Is an kaprekar number\n",number);
}
else
{
//When No
printf("%d Is not a kaprekar number\n",number);
}
}
int main() {
//Test Cases
kaprekar(55);
kaprekar(95);
kaprekar(77);
kaprekar(99);

return 0;
}
```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````
``````/*
C++ Program
Check if a given number is kaprekar number or not
*/
#include<iostream>
#include <math.h>
using namespace std;

class MyNumber {
public:

//Count the number of digits in number
int digit_length(int number) {
int size = 0;
while (number != 0) {
number /= 10;
size++;
}
return size;
}
// Check whether given number is kaprekar number or not
bool is_kaprekar(int number) {
if (number == 1) {
return true;
}
// Calculate square of given number
int square = number *number;
// Get the length of digits in given number square
int size = this->digit_length(square);
int sum = 0;
int parts = 0;
for (int digit = 1; digit < size; ++digit) {
parts = int(pow(10, digit));
if (parts != number) {
// Combine parts of square numbers
sum = (square / parts) + (square % parts);
if (sum == number) {
return true;
}
}
}
return false;
}
void kaprekar(int number) {
if (this->is_kaprekar(number) == true) {
//When Yes

cout << number << " Is an kaprekar number\n";
} else {
//When No

cout << number << " Is not a kaprekar number\n";
}
}
};
int main() {
MyNumber obj ;
//Test Cases
obj.kaprekar(55);
obj.kaprekar(95);
obj.kaprekar(77);
obj.kaprekar(99);
return 0;
}```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````
``````/*
Java Program
Check if a given number is kaprekar number or not
*/

public class MyNumber {

//Count the number of digits in number
public int digit_length(int number)
{
int size = 0;

while (number!=0)
{
number/=10;

size++;
}
return size;
}

// Check whether given number is kaprekar number or not
public boolean is_kaprekar(int number)
{
if (number == 1) {
return true;
}

// Calculate square of given number
int square = number * number;

// Get the length of digits in given number square
int size = digit_length(square);

int sum = 0;

int parts = 0;

for (int digit = 1; digit < size; ++digit)
{
parts = (int)Math.pow(10, digit);

if (parts != number)
{
// Combine parts of square numbers
sum = ( square / parts ) + ( square % parts );

if (sum == number)
{
//When square digit sum is equal to number
return true;
}
}
}

return false;
}

public void kaprekar(int number)
{
if(is_kaprekar(number) == true)
{
//When Yes
System.out.print(number+" Is an kaprekar number\n");
}
else
{
//When No
System.out.print(number+" Is not a kaprekar number\n");
}
}

public static void main(String[] args) {

MyNumber obj = new MyNumber();

//Test Cases
obj.kaprekar(55);
obj.kaprekar(95);
obj.kaprekar(77);
obj.kaprekar(99);

}
}```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````
``````/*
C# Program
Check if a given number is kaprekar number or not
*/
using System;
public class MyNumber {

//Count the number of digits in number
public int digit_length(int number) {
int size = 0;

while (number != 0) {
number /= 10;

size++;
}
return size;
}

// Check whether given number is kaprekar number or not
public Boolean is_kaprekar(int number) {
if (number == 1) {
return true;
}

// Calculate square of given number
int square = number * number;

// Get the.Length of digits in given number square
int size = digit_length(square);

int sum = 0;

int parts = 0;

for (int digit = 1; digit < size; ++digit) {
parts = (int) Math.Pow(10, digit);

if (parts != number) {
// Combine parts of square numbers
sum = (square / parts) + (square % parts);

if (sum == number) {
//When square digit sum is equal to number
return true;
}
}
}

return false;
}

public void kaprekar(int number) {
if (is_kaprekar(number) == true) {
//When Yes
Console.Write(number + " Is an kaprekar number\n");
} else {
//When No
Console.Write(number + " Is not a kaprekar number\n");
}
}

public static void Main(String[] args) {

MyNumber obj = new MyNumber();

//Test Cases
obj.kaprekar(55);
obj.kaprekar(95);
obj.kaprekar(77);
obj.kaprekar(99);

}
}```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````
``````# Python 3 Program
# Check if a given number is kaprekar number or not
class MyNumber :
# Count the number of digits in number
def digit_length(self, number) :
size = 0
while (number != 0) :
number = (number / 10)
size += 1

return size

#  Check whether given number is kaprekar number or not
def is_kaprekar(self, number) :
if (number == 1) :
return True

#  Calculate square of given number
square = number * number
#  Get the length of digits in given number square
size = self.digit_length(square)
sum = 0
parts = 0
digit = 1
while (digit < size) :
parts = 10**digit
if (parts != number) :
#  Combine parts of square numbers
sum = int(square / parts) + (square % parts)
if (sum == number) :
return True

digit += 1

return False

def kaprekar(self, number) :
if (self.is_kaprekar(number) == True) :
print(number ," Is an kaprekar number")
else :
print(number ," Is not a kaprekar number")

def main() :
obj = MyNumber()
obj.kaprekar(55)
obj.kaprekar(95)
obj.kaprekar(77)
obj.kaprekar(99)

if __name__ == "__main__":
main()```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````
``````# Ruby Program
# Check if a given number is kaprekar number or not
class MyNumber
# Count the number of digits in number
def digit_length(number)
size = 0
while (number != 0)
number /= 10
size += 1
end
return size
end
#  Check whether given number is kaprekar number or not
def is_kaprekar(number)
if (number == 1)
return true
end
#  Calculate square of given number
square = number * number
#  Get the length of digits in given number square
size = self.digit_length(square)
sum = 0
parts = 0
digit = 1
while (digit < size)
parts = 10**digit
if (parts != number)
#  Combine parts of square numbers
sum = (square / parts) + (square % parts)
if (sum == number)
return true
end
end
digit += 1
end
return false
end
def kaprekar(number)
if (self.is_kaprekar(number) == true)
print(number ," Is an kaprekar number\n")
else
print(number ," Is not a kaprekar number\n")
end
end
end
def main()
obj = MyNumber.new()
obj.kaprekar(55)
obj.kaprekar(95)
obj.kaprekar(77)
obj.kaprekar(99)
end
main()```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number
``````
``````/*
Scala Program
Check if a given number is kaprekar number or not
*/
class MyNumber {
//Count the number of digits in number
def digit_length(value : Int): Int = {
var size: Int = 0;
var number: Int = value;
while (number != 0) {
number = (number / 10).toInt;
size += 1;
}
return size;
}
// Check whether given number is kaprekar number or not
def is_kaprekar(number: Int): Boolean = {
if (number == 1) {
return true;
}
// Calculate square of given number
var square: Int = number * number;
// Get the length of digits in given number square
var size: Int = this.digit_length(square);
var sum: Int = 0;
var parts: Int = 0;
var digit: Int = 1;
while (digit < size) {
parts = (scala.math.pow(10, digit)).toInt
if (parts != number) {
// Combine parts of square numbers
sum = (square / parts).toInt + (square % parts);
if (sum == number) {
return true;
}
}
digit += 1;
}
return false;
}
def kaprekar(number: Int): Unit = {
if (this.is_kaprekar(number) == true) {
print(s"\$number Is an kaprekar number\n");
} else {
print(s"\$number Is not a kaprekar number\n");
}
}
}
object Main {
def main(args: Array[String]): Unit = {
var obj: MyNumber = new MyNumber();
obj.kaprekar(55);
obj.kaprekar(95);
obj.kaprekar(77);
obj.kaprekar(99);
}
}```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````
``````/*
Swift 4 Program
Check if a given number is kaprekar number or not
*/
import Foundation
class MyNumber {
//Count the number of digits in number
func digit_length(_ value : Int) -> Int {
var size: Int = 0;
var number: Int = value;
while (number != 0) {
number /= 10;
size += 1;
}
return size;
}
// Check whether given number is kaprekar number or not
func is_kaprekar(_ number: Int) -> Bool {
if (number == 1) {
return true;
}
// Calculate square of given number
let square: Int = number * number;
// Get the length of digits in given number square
let size: Int = self.digit_length(square);
var sum: Int = 0;
var parts: Int = 0;
var digit: Int = 1;
while (digit < size) {
parts = Int(pow(Double(10), Double(digit)));
if (parts != number) {
// Combine parts of square numbers
sum = (square / parts) + (square % parts);
if (sum == number) {
return true;
}
}
digit += 1;
}
return false;
}
func kaprekar(_ number: Int) {
if (self.is_kaprekar(number) == true) {
print(number ," Is an kaprekar number");
} else {
print(number ," Is not a kaprekar number");
}
}
}
func main() {
let obj: MyNumber = MyNumber();
obj.kaprekar(55);
obj.kaprekar(95);
obj.kaprekar(77);
obj.kaprekar(99);
}
main();```
```

#### Output

``````55  Is an kaprekar number
95  Is not a kaprekar number
77  Is not a kaprekar number
99  Is an kaprekar number``````
``````<?php
/*
Php Program
Check if a given number is kaprekar number or not
*/
class MyNumber {
//Count the number of digits in number

public 	function digit_length(\$number) {
\$size = 0;
while (\$number != 0) {
\$number = intval(\$number/10);
\$size++;
}
return \$size;
}
// Check whether given number is kaprekar number or not

public 	function is_kaprekar(\$number) {
if (\$number == 1) {
return true;
}
// Calculate square of given number
\$square = \$number *\$number;
// Get the length of digits in given number square
\$size = \$this->digit_length(\$square);
\$sum = 0;
\$parts = 0;
for (\$digit = 1; \$digit < \$size; ++\$digit) {
\$parts = pow(10, \$digit);
if (\$parts != \$number) {
// Combine parts of square numbers
\$sum = intval((\$square / \$parts)) + (\$square % \$parts);
if (\$sum == \$number) {
return true;
}
}
}
return false;
}
public 	function kaprekar(\$number) {
if (\$this->is_kaprekar(\$number) == true) {
//When Yes

echo(\$number ." Is an kaprekar number\n");
} else {
//When No

echo(\$number ." Is not a kaprekar number\n");
}
}
};

function main() {
\$obj = new MyNumber();
//Test Cases

\$obj->kaprekar(55);
\$obj->kaprekar(95);
\$obj->kaprekar(77);
\$obj->kaprekar(99);
}
main();```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````
``````/*
Node Js Program
Check if a given number is kaprekar number or not
*/
class MyNumber {
//Count the number of digits in number
digit_length(number) {
var size = 0;
while (number != 0) {
number = parseInt(number/ 10);
size++;
}
return size;
}
// Check whether given number is kaprekar number or not
is_kaprekar(number) {
if (number == 1) {
return true;
}
// Calculate square of given number
var square = number *number;
// Get the length of digits in given number square
var size = this.digit_length(square);
var sum = 0;
var parts = 0;
for (var digit = 1; digit < size; ++digit) {
parts = parseInt(Math.pow(10, digit));
if (parts != number) {
// Combine parts of square numbers
sum = parseInt(square / parts) + (square % parts);
if (sum == number) {
return true;
}
}
}
return false;
}
kaprekar(number) {
if (this.is_kaprekar(number) == true) {
//When Yes

process.stdout.write(number + " Is an kaprekar number\n");
} else {
//When No

process.stdout.write(number + " Is not a kaprekar number\n");
}
}
}

function main(args) {
var obj = new MyNumber();
//Test Cases
obj.kaprekar(55);
obj.kaprekar(95);
obj.kaprekar(77);
obj.kaprekar(99)
}
main();```
```

#### Output

``````55 Is an kaprekar number
95 Is not a kaprekar number
77 Is not a kaprekar number
99 Is an kaprekar number``````

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