1.
Introduction
2.
What is a Kaprekar Number?
2.1.
Code
2.2.
Java
2.3.
Output
2.4.
Explanation
3.
Use Cases of Kaprekar Number
4.
Pros of Kaprekar Number
5.
Cons of Kaprekar Number
6.
6.1.
How is Kaprekar number calculated?
6.2.
What are the 3 digit Kaprekar numbers?
6.3.
Are all numbers kaprekar numbers?
7.
Conclusion
Last Updated: Mar 27, 2024
Easy

Kaprekar Number

Rahul Singh

Introduction

Do you know that some numbers, when squared, split into two parts and then added together, give the original number? Do you know that they are called kaprekar numbers? If not, then donâ€™t worry. We will clear all your doubts.

In this article, we will discuss about kaprekar number. We will understand it with the help of an example. We will also talk about its use cases. In the end, we will see the pros and cons of the kaprekar number. Moving forward, letâ€™s first understand what a kaprekar number is.

What is a Kaprekar Number?

A kaprekar number is defined as a non-negative integer. This number is named after an Indian mathematician D.R. Kaprekar. He discovered kaprekar numbers in 1949. Whenever a number is squared, and its digits are split into two parts in order to make their sum equal to the original number, then that number is called a kaprekar number. Letâ€™s understand it better with the help of an example.

Letâ€™s suppose we have a number 55.

1. On squaring 55, it will give 3025.

2. Now, splitting it into two parts will give 30 and 25.

3. Now, if we add these two parts together, then we will again get number 55(30+25).

Moving forward, letâ€™s see its program to understand its logic better.

• Java

Java

``class NinjaClass {    static boolean kaprekar(int number) {        if (number == 1)            return true;        int square = number * number;        int s = square;        int count = 0;        for (int i = 1; i < square; i++) {            count++;            square = square / 10;        }                square = s;        for (int digits = 1; digits < count; digits++) {            int equalParts = (int) Math.pow(10, digits);            if (equalParts == number)                continue;            int sum = square / equalParts + square % equalParts;            if (sum == number)                return true;        }        return false;    }    public static void main(String[] args) {            System.out.println("Below are Kaprekar Numbers between 1 and 100.");        for (int i = 1; i < 100; i++)            if (kaprekar(i))                System.out.print(i + " is a kaprekar number\n");    }}``

Explanation

In the above code, we have made a NinjaClass, inside which we have made a function named kaprekar. This function checks whether the number is kaprekar or not and returns true or false on the basis of it. If true is returned, then it prints that particular number is a kaprekar number. According to the above output, we can say that between 1 and 100, there are 5 kaprekar numbers, which are, 1, 9, 45, 55, and 99.

Use Cases of Kaprekar Number

There are various use cases of a kaprekar number. A few of them are mentioned below.

1. Helps in Programming: Kaprekar numbers play an important role in programming. They are used in software development for creating random number generators, testing algorithms, and so on.

2. Used in Cryptography: For cryptographic applications, kaprekar numbers can be used to generate random numbers. As kaprekar numbers have unique properties so it becomes easy to predict or generate random numbers.

3. Recreational Mathematics: Kaprekar numbers are also used in recreational mathematics. They can be a source of challenging puzzles and various interesting problems.

Pros of Kaprekar Number

There are various pros of a kaprekar number. A few of them are mentioned below.

1. Unique Property: Kaprekar numbers have a unique property. Its property of becoming equal to the original number after being squared and adding its digits makes it unique from other numbers.

2. Mathematical Applications: Kaprekar numbers play an important role in mathematics. They can be used in number theory, digital roots, and so on. They own interesting properties in number systems and bases.

3. Used in Computer Science: Along with mathematical applications, kaprekar numbers do play an important role in computer science. They can be used in generating random numbers, testing algorithms, creating unique identification numbers, and so on.

Cons of Kaprekar Number

Below are a few cons of a kaprekar number.

1. Complexity: A kaprekar number is complex. Sometimes, it becomes difficult to understand it. The property of splitting a number into digits and then adding them together again may be confusing for some people.

2. Practical Applications are Limited: The practical applications of kaprekar numbers are limited. They do have some practical applications in computer science and mathematics, but they may not be useful for real-world problems.

3. Rarity: The kaprekar numbers are rare, and sometimes, it becomes difficult to find them and work with them. There is no general or fixed formula to generate a kaprekar number. Beyond a certain range, we may face issues in identifying whether a number is kaprekar or not.

How is Kaprekar number calculated?

A Kaprekar number is calculated by squaring a non-negative integer, splitting its digits into two parts, and summing them. If the sum becomes equal to the original number, it's a Kaprekar number (e.g., 45 is a Kaprekar number because 20 + 25 = 45).

What are the 3 digit Kaprekar numbers?

Three-digit Kaprekar numbers are those 3-digit non-negative integers whose squares, when split into two parts, have a sum equal to the original number. Examples of 3-digit Kaprekar numbers include 297 (2+97=99), 487 (4+87=91), and 999 (9+99=108).

Are all numbers kaprekar numbers?

No, all numbers are not kaprekar numbers. Those numbers that are when squared, split into two parts, and then added together to give the original number are known as kaprekar numbers.

Conclusion

In this article, we have discussed about kaprekar number. We have understood it with the help of an example. We have also talked about its use cases. In the end, we have seen the pros and cons of the kaprekar number. You can also read about prime number.

We hope this article helped you in understanding about kaprekar number. You can read more such articles on our platform, Coding Ninjas Studio. You will find articles on almost every topic on our platform. Also, you can practice coding questions at Coding Ninjas to crack good product-based companies. For interview preparations, you can read the Interview Experiences of popular companies

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