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Product of factors of number

The "Product of Factors of a Number" problem involves finding all the factors of a given positive integer and then calculating their product. A factor of a number is a positive integer that divides the number without leaving a remainder. The product of these factors is simply the result of multiplying all the factors together. In this article, we will explain the problem, provide a suitable example, present the pseudocode and algorithm to solve the problem, and analyze the time complexity of the given code.

Problem Statement

Given a positive integer num, we need to find all the factors of num and then calculate their product.

Example

Let's take an example to illustrate the problem. Consider the number 20. Factors of 20 are: 1, 2, 4, 5, 10, and 20. Product of factors = 1 * 2 * 4 * 5 * 10 * 20 = 800

Pseudocode

factorProduct(num)
    result = num
    for i = 2 to num/2
        if num is divisible by i
            print i
            result = result * i
    print num
    print "Factors Product :", result

Algorithm Explanation

  1. Start by initializing the variable result to the value of num. This variable will store the product of factors.
  2. Loop through all integers i from 2 to num/2. We start from 2 because every number is divisible by 1, and we go up to num/2 because any factor greater than num/2 would result in a quotient less than 2, which means it's not a factor.
  3. Inside the loop, check if num is divisible by i using the modulo operator (num % i == 0). If the condition is true, it means i is a factor of num.
  4. Print the value of i, as it is one of the factors.
  5. Update the result by multiplying it with the factor i.
  6. After the loop, print the value of num to include it as one of the factors.
  7. Print the final result, which is the product of all the factors stored in the result variable.

Code Solution

Here given code implementation process.

// C Program
// Product of factors of number
#include <stdio.h>

// Calculate factors product of a number
void factorProduct(int num)
{
	printf("\n Factors of a number %d is \n", num);
	int result = num;
	// Execute loop through by 2 to num/2
	for (int i = 2; i <= num / 2; ++i)
	{
		if (num % i == 0)
		{
			printf(" %d", i);
			// calculated product 
			result *= i;
		}
	}
	// Last factors
	printf(" %d", num);
	// Display calculated result
	printf("\n Factors Product : %d\n", result);
}
int main()
{
	// Test Cases
	factorProduct(15);
	factorProduct(40);
	factorProduct(31);
	return 0;
}

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31
/*
   Java Program
   Product of factors of number
*/
public class Factorization
{
	// Calculate factors product of a number
	public void factorProduct(int num)
	{
		System.out.print("\n Factors of a number " + num + " is \n");
		int result = num;
		// Execute loop through by 2 to num/2
		for (int i = 2; i <= num / 2; ++i)
		{
			if (num % i == 0)
			{
				System.out.print(" " + i);
				// calculated product 
				result *= i;
			}
		}
		// Last factors
		System.out.print(" " + num);
		// Display calculated result
		System.out.print("\n Factors Product : " + result + "\n");
	}
	public static void main(String[] args)
	{
		Factorization task = new Factorization();
		// Test Cases
		task.factorProduct(15);
		task.factorProduct(40);
		task.factorProduct(31);
	}
}

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31
// Include header file
#include <iostream>
using namespace std;

/*
   C++ Program
   Product of factors of number
*/

class Factorization
{
	public:
		// Calculate factors product of a number
		void factorProduct(int num)
		{
			cout << "\n Factors of a number " << num << " is \n";
			int result = num;
			// Execute loop through by 2 to num/2
			for (int i = 2; i <= num / 2; ++i)
			{
				if (num % i == 0)
				{
					cout << " " << i;
					// calculated product
					result *= i;
				}
			}
			// Last factors
			cout << " " << num;
			// Display calculated result
			cout << "\n Factors Product : " << result << "\n";
		}
};
int main()
{
	Factorization task = Factorization();
	// Test Cases
	task.factorProduct(15);
	task.factorProduct(40);
	task.factorProduct(31);
	return 0;
}

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31
// Include namespace system
using System;
/*
   C# Program
   Product of factors of number
*/
public class Factorization
{
	// Calculate factors product of a number
	public void factorProduct(int num)
	{
		Console.Write("\n Factors of a number " + num + " is \n");
		int result = num;
		// Execute loop through by 2 to num/2
		for (int i = 2; i <= num / 2; ++i)
		{
			if (num % i == 0)
			{
				Console.Write(" " + i);
				// calculated product
				result *= i;
			}
		}
		// Last factors
		Console.Write(" " + num);
		// Display calculated result
		Console.Write("\n Factors Product : " + result + "\n");
	}
	public static void Main(String[] args)
	{
		Factorization task = new Factorization();
		// Test Cases
		task.factorProduct(15);
		task.factorProduct(40);
		task.factorProduct(31);
	}
}

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31
<?php
/*
   Php Program
   Product of factors of number
*/
class Factorization
{
	// Calculate factors product of a number
	public	function factorProduct($num)
	{
		echo "\n Factors of a number ". $num ." is \n";
		$result = $num;
		// Execute loop through by 2 to num/2
		for ($i = 2; $i <= intval($num / 2); ++$i)
		{
			if ($num % $i == 0)
			{
				echo " ". $i;
				// calculated product
				$result *= $i;
			}
		}
		// Last factors
		echo " ". $num;
		// Display calculated result
		echo "\n Factors Product : ". $result ."\n";
	}
}

function main()
{
	$task = new Factorization();
	// Test Cases
	$task->factorProduct(15);
	$task->factorProduct(40);
	$task->factorProduct(31);
}
main();

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31
/*
   Node Js Program
   Product of factors of number
*/
class Factorization
{
	// Calculate factors product of a number
	factorProduct(num)
	{
		process.stdout.write("\n Factors of a number " + num + " is \n");
		var result = num;
		// Execute loop through by 2 to num/2
		for (var i = 2; i <= parseInt(num / 2); ++i)
		{
			if (num % i == 0)
			{
				process.stdout.write(" " + i);
				// calculated product
				result *= i;
			}
		}
		// Last factors
		process.stdout.write(" " + num);
		// Display calculated result
		process.stdout.write("\n Factors Product : " + result + "\n");
	}
}

function main()
{
	var task = new Factorization();
	// Test Cases
	task.factorProduct(15);
	task.factorProduct(40);
	task.factorProduct(31);
}
main();

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31
#  Python 3 Program
#  Product of factors of number

class Factorization :
	#  Calculate factors product of a number
	def factorProduct(self, num) :
		print("\n Factors of a number ", num ," is ")
		result = num
		i = 2
		#  Execute loop through by 2 to num/2
		while (i <= int(num / 2)) :
			if (num % i == 0) :
				print(" ", i, end = "")
				#  calculated product
				result *= i
			
			i += 1
		
		#  Last factors
		print(" ", num, end = "")
		#  Display calculated result
		print("\n Factors Product :", result )
	

def main() :
	task = Factorization()
	#  Test Cases
	task.factorProduct(15)
	task.factorProduct(40)
	task.factorProduct(31)

if __name__ == "__main__": main()

Output

 Factors of a number  15  is
  3  5  15
 Factors Product : 225

 Factors of a number  40  is
  2  4  5  8  10  20  40
 Factors Product : 2560000

 Factors of a number  31  is
  31
 Factors Product : 31
# Ruby Program
# Product of factors of number

class Factorization 
	#  Calculate factors product of a number
	def factorProduct(num) 
		print("\n Factors of a number ", num ," is \n")
		result = num
		i = 2
		#  Execute loop through by 2 to num/2
		while (i <= num / 2) 
			if (num % i == 0) 
				print(" ", i)
				#  calculated product
				result *= i
			end

			i += 1
		end

		#  Last factors
		print(" ", num)
		#  Display calculated result
		print("\n Factors Product : ", result ,"\n")
	end

end

def main() 
	task = Factorization.new()
	#  Test Cases
	task.factorProduct(15)
	task.factorProduct(40)
	task.factorProduct(31)
end

main()

Output

 Factors of a number 15 is 
 3 5 15
 Factors Product : 225

 Factors of a number 40 is 
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is 
 31
 Factors Product : 31

/*
   Scala Program
   Product of factors of number
*/
class Factorization
{
	// Calculate factors product of a number
	def factorProduct(num: Int): Unit = {
		print("\n Factors of a number " + num + " is \n");
		var result: Int = num;
		var i: Int = 2;
		// Execute loop through by 2 to num/2
		while (i <= (num / 2).toInt)
		{
			if (num % i == 0)
			{
				print(" " + i);
				// calculated product
				result *= i;
			}
			i += 1;
		}
		// Last factors
		print(" " + num);
		// Display calculated result
		print("\n Factors Product : " + result + "\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Factorization = new Factorization();
		// Test Cases
		task.factorProduct(15);
		task.factorProduct(40);
		task.factorProduct(31);
	}
}

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31
/*
   Swift 4 Program
   Product of factors of number
*/
class Factorization
{
	// Calculate factors product of a number
	func factorProduct(_ num: Int)
	{
		print("\n Factors of a number ", num ," is ");
		var result: Int = num;
		var i: Int = 2;
		// Execute loop through by 2 to num/2
		while (i <= num / 2)
		{
			if (num % i == 0)
			{
				print(" ", i, terminator: "");
				// calculated product
				result *= i;
			}
			i += 1;
		}
		// Last factors
		print(" ", num, terminator: "");
		// Display calculated result
		print("\n Factors Product : ", result );
	}
}
func main()
{
	let task: Factorization = Factorization();
	// Test Cases
	task.factorProduct(15);
	task.factorProduct(40);
	task.factorProduct(31);
}
main();

Output

 Factors of a number  15  is
  3  5  15
 Factors Product :  225

 Factors of a number  40  is
  2  4  5  8  10  20  40
 Factors Product :  2560000

 Factors of a number  31  is
  31
 Factors Product :  31
/*
   Kotlin Program
   Product of factors of number
*/
class Factorization
{
	// Calculate factors product of a number
	fun factorProduct(num: Int): Unit
	{
		print("\n Factors of a number " + num + " is \n");
		var result: Int = num;
		var i: Int = 2;
		// Execute loop through by 2 to num/2
		while (i <= num / 2)
		{
			if (num % i == 0)
			{
				print(" " + i);
				// calculated product
				result *= i;
			}
			i += 1;
		}
		// Last factors
		print(" " + num);
		// Display calculated result
		print("\n Factors Product : " + result + "\n");
	}
}
fun main(args: Array < String > ): Unit
{
	var task: Factorization = Factorization();
	// Test Cases
	task.factorProduct(15);
	task.factorProduct(40);
	task.factorProduct(31);
}

Output

 Factors of a number 15 is
 3 5 15
 Factors Product : 225

 Factors of a number 40 is
 2 4 5 8 10 20 40
 Factors Product : 2560000

 Factors of a number 31 is
 31
 Factors Product : 31

Resultant Output Explanation

let's evaluate the output for the given test cases:

  1. factorProduct(15);

    • Factors of 15 are: 3, 5, 15
    • Product of factors = 3 * 5 * 15 = 225

  2. factorProduct(40);

    • Factors of 40 are: 2, 4, 5, 8, 10, 20, 40
    • Product of factors = 2 * 4 * 5 * 8 * 10 * 20 * 40 = 2560000

  3. factorProduct(31);

    • Factors of 31 are: 31
    • Product of factors = 31

Time Complexity

Let's analyze the time complexity of the given code. The loop runs from 2 to num/2, so its time complexity can be considered as O(num/2). However, the constant factor is ignored in Big O notation. Hence, the time complexity of the code is approximately O(num).

In simple terms, the time taken by the code to calculate the product of factors depends linearly on the input num. As num grows larger, the time taken by the code also grows linearly.

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