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Abundant Number

The problem being addressed is to determine whether a given number is an abundant number or not. An abundant number is a positive integer that is smaller than the sum of its proper divisors (excluding itself). This concept is used to classify numbers based on their properties and relationships with their divisors.

Problem Statement and Description

Given a positive integer, the goal is to determine whether it is an abundant number or not. An abundant number is one where the sum of its proper divisors is greater than the number itself. For instance, the number 20 has divisors 1, 2, 4, 5, and 10. The sum of these divisors is 22, which is greater than 20, making 20 an abundant number.

Idea to Solve the Problem

To determine if a number is abundant or not, we can calculate the sum of its proper divisors and compare it with the number itself. If the sum is greater, the number is abundant; otherwise, it is not.

Pseudocode

divisor_sum(number):
    result = 0
    for i from 1 to number/2:
        if number % i == 0:
            result += i
    return result

is_abundant(number):
    if divisor_sum(number) > number:
        print number, "Is an Abundant Number"
    else:
        print number, "Is not an Abundant Number"

main():
    is_abundant(20)
    is_abundant(11)
    is_abundant(104)

Algorithm Explanation

  1. Create a function divisor_sum(number) that calculates the sum of the proper divisors of the given number. Iterate through numbers from 1 to number/2. If the current number divides number evenly (i.e., number % i == 0), add it to the result.
  2. Create a function is_abundant(number) that determines whether a number is abundant or not. Call the divisor_sum function to get the sum of proper divisors. Compare the sum with the number itself. If the sum is greater, print that the number is an abundant number; otherwise, print that it is not.
  3. In the main() function, call is_abundant for different test cases.

Code Solution

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

// Function which is calculate sum of divisors in given number  
int divisor_sum(int number) 
{ 
  int result = 0; 

  for (int i=1; i<= number/2; i++) 
  { 
    if (number%i==0) 
    { 
      //When number is divide by i
      result += i;
    } 
  } 

  return result; 
} 
//Function are show the result number is abundant or not
void is_abundant(int number) 
{ 
  //Check whether number divisor sum is greater than given number?
  if(divisor_sum(number) > number)
  {
    //When Yes
    printf("%d Is an Abundant Number\n",number);
  } 
  else
  {
    //When No
    printf("%d Is not a Abundant Number\n",number);
  }
} 

int main() {
  //Test Cases
  is_abundant(20);
  is_abundant(11);
  is_abundant(104);
  return 0;
}

Output

20 Is an Abundant Number
11 Is not a Abundant Number
104 Is an Abundant Number
/*
 C++ Program
 Check if a given number is abundant or not
*/
#include<iostream>

using namespace std;

class MyNumber {
	public:

		// Function which is calculate sum of divisors in given number  
		int divisor_sum(int number) {
			int result = 0;
			for (int i = 1; i <= number / 2; i++) {
				if (number % i == 0) {
					//When number is divide by i
					result += i;
				}
			}
			return result;
		}
	//Function are show the result number is abundant or not
	void is_abundant(int number) {
		//Check whether number divisor sum is greater than given number?

		if (this->divisor_sum(number) > number) {
			//When Yes

			cout << number << " Abundant Number\n";
		} else {
			//When No

			cout << number << " Is not a Abundant Number\n";
		}
	}
};
int main() {
	MyNumber obj ;
	// Test Case
	obj.is_abundant(20);
	obj.is_abundant(11);
	obj.is_abundant(104);
	return 0;
}

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number
/*
  Java Program
  Check if a given number is abundant or not
*/

public class MyNumber {

  // Function which is calculate sum of divisors in given number  
  public int divisor_sum(int number) 
  { 
    int result = 0; 

    for (int i=1; i<= number/2; i++) 
    { 
      if (number%i==0) 
      { 
        //When number is divide by i
        result += i;
      } 
    } 

    return result; 
  } 
  //Function are show the result number is abundant or not
  public void is_abundant(int number) 
  { 
    //Check whether number divisor sum is greater than given number?
    if(divisor_sum(number) > number)
    {
      //When Yes
     System.out.print(number+" Abundant Number\n");
    } 
    else
    {
      //When No
     System.out.print(number+" Is not a Abundant Number\n");
    }
  } 
  public static void main(String[] args) {

    MyNumber obj = new MyNumber();
    // Test Case
    obj.is_abundant(20);
    obj.is_abundant(11);
    obj.is_abundant(104);
  }
}

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number
/*
  C# Program
  Check if a given number is abundant or not
*/
using System;
public class MyNumber {

	// Function which is calculate sum of divisors in given number  
	public int divisor_sum(int number) {
		int result = 0;

		for (int i = 1; i <= number / 2; i++) {
			if (number % i == 0) {
				//When number is divide by i
				result += i;
			}
		}

		return result;
	}
	//Function are show the result number is abundant or not
	public void is_abundant(int number) {
		//Check whether number divisor sum is greater than given number?
		if (divisor_sum(number) > number) {
			//When Yes
			Console.Write(number + " Abundant Number\n");
		} else {
			//When No
			Console.Write(number + " Is not a Abundant Number\n");
		}
	}
	public static void Main(String[] args) {

		MyNumber obj = new MyNumber();
		// Test Case
		obj.is_abundant(20);
		obj.is_abundant(11);
		obj.is_abundant(104);
	}
}

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number
# Python 3 Program
# Java Program
class MyNumber :
	# Function which is calculate sum of divisors in given number  
	def divisor_sum(self, number) :
		result = 0
		i = 1
		while (i <= int(number / 2)) :
			if (number % i == 0) :
				#When number is divide by i
				result += i
			
			i += 1
		
		return result
	
	#Function are show the result number is abundant or not
	def is_abundant(self, number) :
		#Check whether number divisor sum is greater than given number?

		if (self.divisor_sum(number) > number) :
			print(number ," Abundant Number")
		else :
			print(number ," Is not a Abundant Number")
		
	

def main() :
	obj = MyNumber()
	obj.is_abundant(20)
	obj.is_abundant(11)
	obj.is_abundant(104)


if __name__ == "__main__":
	main()

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number
# Ruby Program 
# Check if a given number is abundant or not

class MyNumber 
	# Function which is calculate sum of divisors in given number  
	def divisor_sum(number) 
		result = 0
		i = 1
		while (i <= number / 2) 
			if (number % i == 0) 
				#When number is divide by i
				result += i
			end
			i += 1
		end
		return result
	end
	#Function are show the result, number is abundant or not
	def is_abundant(number) 
		#Check whether number divisor sum is greater than given number?

		if (self.divisor_sum(number) > number) 
			print(number ," Abundant Number\n")
		else 
			print(number ," Is not a Abundant Number\n")
		end
	end
end
def main() 
	obj = MyNumber.new()
	obj.is_abundant(20)
	obj.is_abundant(11)
	obj.is_abundant(104)
end
main()

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number

/*
 Scala Program
  Check if a given number is abundant or not
*/
class MyNumber {
	// Function which is calculate sum of divisors in given number  
	def divisor_sum(number: Int): Int = {
		var result: Int = 0;
		var i: Int = 1;
		while (i <= number / 2) {
			if (number % i == 0) {
				//When number is divide by i
				result += i;
			}
			i += 1;
		}
		return result;
	}
	//Function are show the result number is abundant or not
	def is_abundant(number: Int): Unit = {
		//Check whether number divisor sum is greater than given number?

		if (this.divisor_sum(number) > number) {
			print(s"$number Abundant Number\n");
		} else {
			print(s"$number Is not a Abundant Number\n");
		}
	}
}
object Main {
	def main(args: Array[String]): Unit = {
		var obj: MyNumber = new MyNumber();
        obj.is_abundant(20);
        obj.is_abundant(11);
        obj.is_abundant(104);
	}
}

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number
/*
  Swift 4 Program
  Check if a given number is abundant or not
*/
class MyNumber {
	// Function which is calculate sum of divisors in given number  
	func divisor_sum(_ number: Int) -> Int {
		var result: Int = 0;
		var i: Int = 1;
		while (i <= number / 2) {
			if (number % i == 0) {
				//When number is divide by i
				result += i;
			}
			i += 1;
		}
		return result;
	}
	//Function are show the result number is abundant or not
	func is_abundant(_ number: Int) {
		//Check whether number divisor sum is greater than given number?

		if (self.divisor_sum(number) > number) {
			print(number ," Abundant Number");
		} else {
			print(number ," Is not a Abundant Number");
		}
	}
}
func main() {
	let obj: MyNumber = MyNumber();
	obj.is_abundant(20);
	obj.is_abundant(11);
	obj.is_abundant(104);
}
main();

Output

20  Abundant Number
11  Is not a Abundant Number
104  Abundant Number
<?php
/*
  Php Program
  Check if a given number is abundant or not
*/
class MyNumber {
	// Function which is calculate sum of divisors in given number  

	public 	function divisor_sum($number) {
		$result = 0;
		for ($i = 1; $i <= intval($number / 2); $i++) {
			if ($number % $i == 0) {
				//When number is divide by i
				$result += $i;
			}
		}
		return $result;
	}
	//Function are show the result number is abundant or not

	public 	function is_abundant($number) {
		//Check whether number divisor sum is greater than given number?

		if ($this->divisor_sum($number) > $number) {
			//When Yes

			echo($number ." Abundant Number\n");
		} else {
			//When No

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

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

	$obj->is_abundant(20);
	$obj->is_abundant(11);
	$obj->is_abundant(104);
}
main();

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number
/*
 Node Js Program
 Check if a given number is abundant or not
*/
class MyNumber {
	// Function which is calculate sum of divisors in given number  
	divisor_sum(number) {
		var result = 0;
		for (var i = 1; i <= parseInt(number / 2); i++) {
			if (number % i == 0) {
				//When number is divide by i
				result += i;
			}
		}
		return result;
	}
	//Function are show the result number is abundant or not
	is_abundant(number) {
		//Check whether number divisor sum is greater than given number?

		if (this.divisor_sum(number) > number) {
			//When Yes

			process.stdout.write(number + " Abundant Number\n");
		} else {
			//When No

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

function main(args) {
	var obj = new MyNumber();
	// Test Case
	obj.is_abundant(20);
	obj.is_abundant(11);
	obj.is_abundant(104)
}
main();

Output

20 Abundant Number
11 Is not a Abundant Number
104 Abundant Number

Time Complexity Analysis

For a given number n, the divisor_sum function iterates through numbers from 1 to n/2, checking for divisibility. Therefore, the time complexity of the divisor_sum function is O(n/2), which simplifies to O(n). The is_abundant function calls divisor_sum and performs a constant-time comparison. Overall, the algorithm's time complexity is O(n), where n is the given number.

Last updated on by Kalkicode




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