PHP Program to Check Smith Number

Posted in PHP Tutorial

Updated on Oct 31, 2024

By Mari Selvan

👁️ 39 - 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 PHP program that checks whether a given number is a Smith Number.

📄 Example

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

isSmithNumber.php

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

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

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

  return $sum;
}

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

// Replace this value with your desired number
$number = 85;

// Check if the number is a Smith Number
if (isSmithNumber($number))
{
  echo "$number is a Smith Number.\n";
}
else
{
  echo "$number is not a Smith Number.\n";
}

?>

💻 Testing the Program

To test the program with different numbers, replace the value of $number.

Output

85 is a Smith Number.

Run the script 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 value of $number is replaced with the desired number, and the program 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 php code that checks for Smith Numbers in the specified range.

isSmithNumber.php

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

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

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

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

// Check numbers from 1 to 100
echo "Smith Numbers in the Range 1 to 100:\n";
for ($i = 1;$i <= 100;++$i)
{
  if (isSmithNumber($i))
  {
    echo "$i ";
  }
}
echo "\n";

?>

💻 Testing the Program

Output

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

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!