C++ Program to Check Smith Number

Posted in C++ Tutorial

Updated on Oct 06, 2024

By Mari Selvan

👁️ 98 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In the realm of programming, exploring number properties is a common and fascinating endeavor. One interesting type of number is the Smith Number.

A Smith Number is a composite number for which the sum of its digits is equal to the sum of the digits in its prime factorization.

In this tutorial, we'll delve into a C++ program that checks whether a given number is a Smith Number.

📄 Example

Let's take a look at the C++ code that checks whether a given number is a Smith Number.

isSmithNumber.cpp

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#include <iostream>
#include <vector>

// Function to calculate the sum of digits in a number
int sumOfDigits(int num) {
  int sum = 0;
  while (num > 0) {
    sum += num % 10;
    num /= 10;
  }
  return sum;
}

// Function to calculate the sum of digits in the prime factorization of a number
int sumOfPrimeFactors(int num) {
  int i = 2, sum = 0;

  while (num > 1) {
    while (num % i == 0) {
      sum += sumOfDigits(i);
      num /= i;
    }
    i++;
  }

  return sum;
}

// Function to check if a number is a Smith Number
bool isSmithNumber(int num) {
  return sumOfDigits(num) == sumOfPrimeFactors(num);
}

// Driver program
int main() {
  // Replace this value with your desired number
  int number = 85;

  // Check if the number is a Smith Number
  if (isSmithNumber(number)) {
    std::cout << number << " is a Smith Number." << std::endl;
  } else {
    std::cout << number << " is not a Smith Number." << std::endl;
  }

  return 0;
}

💻 Testing the Program

To test the program with different numbers, replace the value of number in the main function.

Output

85 is a Smith Number.

Compile and run the program to check whether the given number is a Smith Number.

🧠 How the Program Works

The program defines three functions: sumOfDigits to calculate the sum of digits in a number, sumOfPrimeFactors to calculate the sum of digits in the prime factorization, and isSmithNumber to check if a number is a Smith Number.
The main function replaces the value of number with the desired number and checks if it is a Smith Number.
The program utilizes loops and arithmetic operations to calculate the sum of digits and the sum of digits in the prime factorization.

📏 Between the Given Range

Let's take a look at the C++ code that checks for Smith Numbers in the specified range.

isSmithNumber.cpp

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#include <iostream>
#include <cmath>

// Function to calculate the sum of digits
int sumOfDigits(int n) {
  int sum = 0;
  while (n > 0) {
    sum += n % 10;
    n /= 10;
  }
  return sum;
}

// Function to calculate the sum of prime factors
int sumOfPrimeFactors(int n) {
  int sum = 0;
  for (int i = 2; i <= n; ++i) {
    while (n % i == 0) {
      sum += sumOfDigits(i);
      n /= i;
    }
  }
  return sum;
}

// Function to check if a number is prime
bool isPrime(int n) {
  if (n <= 1) {
    return false;
  }
  for (int i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}

// Function to check if a number is a Smith Number
bool isSmithNumber(int n) {
  return isPrime(n) ? false : sumOfDigits(n) == sumOfPrimeFactors(n);
}

// Driver program
int main() {
  std::cout << "Smith Numbers in the Range 1 to 100:" << std::endl;

  // Check numbers from 1 to 100
  for (int i = 1; i <= 100; ++i) {
    if (isSmithNumber(i)) {
      std::cout << i << " ";
    }
  }

  std::cout << std::endl;

  return 0;
}

💻 Testing the Program

Output

Smith Numbers in the Range 1 to 100:
4 22 27 58 85 94

Compile and run the program to see the Smith Numbers in the specified range.

🧠 How the Program Works

The program defines a function isPrime to check if a number is prime.
The isSmithNumber function checks if a number is a Smith Number by comparing the sum of its digits with the sum of the digits in its prime factorization.
The main function checks and prints Smith Numbers in the range from 1 to 100.

🧐 Understanding the Concept of Smith Numbers

Before delving into the code, it's crucial to understand the concept of Smith Numbers. These numbers exhibit a unique property where the sum of their digits is equal to the sum of the digits in their prime factorization.

For example, 4, 22, 27, and 85 are Smith Numbers.

🎢 Optimizing the Program

While the provided program is effective, consider exploring optimizations for larger numbers. You can further refine the code for improved efficiency or adapt it to your specific requirements.

Feel free to incorporate and modify this code as needed for your specific use case. Happy coding!