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Code Mathematics

Check that if large number is divisible by 2

The problem at hand revolves around determining whether a large number is divisible by 2 or not. Divisibility by 2 is a fundamental mathematical concept that is frequently used in programming to optimize various algorithms and processes. When a number is divisible by 2, it means it can be evenly divided by 2 without leaving a remainder. In the context of computer programming, this often involves analyzing the last digit of a number to determine its divisibility by 2.

Problem Statement and Description

Given a large number represented as a string, we want to determine if the number is divisible by 2. The approach to solving this problem involves checking the last digit of the number and examining whether it is an even digit (0, 2, 4, 6, or 8). If the last digit is even, then the number is divisible by 2; otherwise, it's not.

Example

Let's consider the number "123456". The last digit is 6, which is an even number. Therefore, the number 123456 is divisible by 2.

Idea to Solve the Problem

  1. Convert the given number to a string.
  2. Get the last digit of the string representation of the number.
  3. Check if the last digit is one of the even digits (0, 2, 4, 6, 8).

Test Cases

  1. Input

    "122938934834534345345343940"
    Output
    Divisible by 2
    Explanation
    The last digit is 0, which is even.

  2. Input

    "2342348234"
    Output
    Divisible by 2
    Explanation
    The last digit is 4, which is even.

  3. Input

    "2398231234233251"
    Output
    Not divisible by 2
    Explanation
    The last digit is 1, which is not even.

  4. Input

    "33282949823493"
    Output
    Not divisible by 2
    Explanation
    The last digit is 3, which is not even.

Pseudocode

function isDivisibleBy2(num):
    last_digit = num.charAt(num.length - 1)
    if last_digit is '0' or '2' or '4' or '6' or '8':
        return true
    else:
        return false

Algorithm Explanation

  1. Start by obtaining the last digit of the given number.
  2. Check if the last digit is any of the even digits ('0', '2', '4', '6', '8').
  3. If the condition is satisfied, return true, indicating that the number is divisible by 2. Otherwise, return false.

Program Solution

// Java program for
// Check that if large number is divisible by 2
public class Divisibility
{
	public void isDivisibleBy2(String num)
	{
		// Condition
		// ➀ Last digit should be a Even number
		boolean result = false;
		int n = num.length();
		if (n == 1 && num.charAt(0) == '0')
		{
			// Given number is zero
			result = true;
		}
		else if (n > 0)
		{
			if (num.charAt(n - 1) == '0' 
                || num.charAt(n - 1) == '2' 
                || num.charAt(n - 1) == '4' 
                || num.charAt(n - 1) == '6' 
                || num.charAt(n - 1) == '8')
			{
				result = true;
			}
		}
		if (result == true)
		{
			System.out.print(" Given number (" + 
                             num + ") is divisible by 2\n");
		}
		else
		{
			System.out.print(" Given number (" + 
                             num + ") is not divisible by 2\n");
		}
	}
	public static void main(String[] args)
	{
		Divisibility task = new Divisibility();
		// Test
		task.isDivisibleBy2("122938934834534345345343940");
		task.isDivisibleBy2("2342348234");
		task.isDivisibleBy2("2398231234233251");
		task.isDivisibleBy2("33282949823493");
	}
}

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2
// Include header file
#include <iostream>
#include <string>
using namespace std;
// C++ program for
// Check that if large number is divisible by 2
class Divisibility
{
	public: void isDivisibleBy2(string num)
	{
		// Condition
		// ➀ Last digit should be a Even number
		bool result = false;
		int n = num.length();
		if (n == 1 && num[0] == '0')
		{
			// Given number is zero
			result = true;
		}
		else if (n > 0)
		{
			if (num[n - 1] == '0' || 
                num[n - 1] == '2' || 
                num[n - 1] == '4' || 
                num[n - 1] == '6' || 
                num[n - 1] == '8')
			{
				result = true;
			}
		}
		if (result == true)
		{
			cout << " Given number (" << num << ") is divisible by 2\n";
		}
		else
		{
			cout << " Given number (" << num << ") is not divisible by 2\n";
		}
	}
};
int main()
{
	Divisibility *task = new Divisibility();
	// Test
	task->isDivisibleBy2("122938934834534345345343940");
	task->isDivisibleBy2("2342348234");
	task->isDivisibleBy2("2398231234233251");
	task->isDivisibleBy2("33282949823493");
	return 0;
}

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2
// Include namespace system
using System;
// Csharp program for
// Check that if large number is divisible by 2
public class Divisibility
{
	public void isDivisibleBy2(String num)
	{
		// Condition
		// ➀ Last digit should be a Even number
		Boolean result = false;
		int n = num.Length;
		if (n == 1 && num[0] == '0')
		{
			// Given number is zero
			result = true;
		}
		else if (n > 0)
		{
			if (num[n - 1] == '0' || num[n - 1] == '2' || num[n - 1] == '4' || num[n - 1] == '6' || num[n - 1] == '8')
			{
				result = true;
			}
		}
		if (result == true)
		{
			Console.Write(" Given number (" + num + ") is divisible by 2\n");
		}
		else
		{
			Console.Write(" Given number (" + num + ") is not divisible by 2\n");
		}
	}
	public static void Main(String[] args)
	{
		Divisibility task = new Divisibility();
		// Test
		task.isDivisibleBy2("122938934834534345345343940");
		task.isDivisibleBy2("2342348234");
		task.isDivisibleBy2("2398231234233251");
		task.isDivisibleBy2("33282949823493");
	}
}

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2
package main

import "fmt"
// Go program for
// Check that if large number is divisible by 2

func isDivisibleBy2(num string) {
	// Condition
	// ➀ Last digit should be a Even number
	var result bool = false
	var n int = len(num)
	if n == 1 && num[0] == '0' {
		// Given number is zero
		result = true
	} else if n > 0 {
		if num[n - 1] == '0' || 
		   num[n - 1] == '2' || 
		   num[n - 1] == '4' || 
		   num[n - 1] == '6' || 
		   num[n - 1] == '8' {
			result = true
		}
	}
	if result == true {
		fmt.Println(" Given number (", num, ") is divisible by 2")
	} else {
		fmt.Println(" Given number (", num, ") is not divisible by 2")
	}
}
func main() {

	// Test
	isDivisibleBy2("122938934834534345345343940")
	isDivisibleBy2("2342348234")
	isDivisibleBy2("2398231234233251")
	isDivisibleBy2("33282949823493")
}

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2
<?php
// Php program for
// Check that if large number is divisible by 2
class Divisibility
{
	public	function isDivisibleBy2($num)
	{
		// Condition
		// ➀ Last digit should be a Even number
		$result = false;
		$n = strlen($num);
		if ($n == 1 && $num[0] == '0')
		{
			// Given number is zero
			$result = true;
		}
		else if ($n > 0)
		{
			if ($num[$n - 1] == '0' || 
                $num[$n - 1] == '2' || 
                $num[$n - 1] == '4' || 
                $num[$n - 1] == '6' || 
                $num[$n - 1] == '8')
			{
				$result = true;
			}
		}
		if ($result == true)
		{
			echo(" Given number (".$num.
				") is divisible by 2\n");
		}
		else
		{
			echo(" Given number (".$num.
				") is not divisible by 2\n");
		}
	}
}

function main()
{
	$task = new Divisibility();
	// Test
	$task->isDivisibleBy2("122938934834534345345343940");
	$task->isDivisibleBy2("2342348234");
	$task->isDivisibleBy2("2398231234233251");
	$task->isDivisibleBy2("33282949823493");
}
main();

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2
// Node JS program for
// Check that if large number is divisible by 2
class Divisibility
{
	isDivisibleBy2(num)
	{
		// Condition
		// ➀ Last digit should be a Even number
		var result = false;
		var n = num.length;
		if (n == 1 && num.charAt(0) == '0')
		{
			// Given number is zero
			result = true;
		}
		else if (n > 0)
		{
			if (num.charAt(n - 1) == '0' || 
                num.charAt(n - 1) == '2' || 
                num.charAt(n - 1) == '4' || 
                num.charAt(n - 1) == '6' || 
                num.charAt(n - 1) == '8')
			{
				result = true;
			}
		}
		if (result == true)
		{
			console.log(" Given number (" + num + ") is divisible by 2");
		}
		else
		{
			console.log(" Given number (" + num + ") is not divisible by 2");
		}
	}
}

function main()
{
	var task = new Divisibility();
	// Test
	task.isDivisibleBy2("122938934834534345345343940");
	task.isDivisibleBy2("2342348234");
	task.isDivisibleBy2("2398231234233251");
	task.isDivisibleBy2("33282949823493");
}
main();

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2
#  Python 3 program for
#  Check that if large number is divisible by 2
class Divisibility :
	def isDivisibleBy2(self, num) :
		#  Condition
		#  ➀ Last digit should be a Even number
		result = False
		n = len(num)
		if (n == 1 and num[0] == '0') :
			#  Given number is zero
			result = True
		elif (n > 0) :
			if (num[n - 1] == '0'
				or num[n - 1] == '2'
				or num[n - 1] == '4'
				or num[n - 1] == '6'
				or num[n - 1] == '8') :
				result = True
			
		
		if (result == True) :
			print(" Given number (", num ,") is divisible by 2")
		else :
			print(" Given number (", num ,") is not divisible by 2")
		
	

def main() :
	task = Divisibility()
	#  Test
	task.isDivisibleBy2("122938934834534345345343940")
	task.isDivisibleBy2("2342348234")
	task.isDivisibleBy2("2398231234233251")
	task.isDivisibleBy2("33282949823493")

if __name__ == "__main__": main()

Output

 Given number ( 122938934834534345345343940 ) is divisible by 2
 Given number ( 2342348234 ) is divisible by 2
 Given number ( 2398231234233251 ) is not divisible by 2
 Given number ( 33282949823493 ) is not divisible by 2
#  Ruby program for
#  Check that if large number is divisible by 2
class Divisibility 
	def isDivisibleBy2(num) 
		#  Condition
		#  ➀ Last digit should be a Even number
		result = false
		n = num.length
		if (n == 1 && num[0] == '0') 
			#  Given number is zero
			result = true
		elsif (n > 0) 
			if (num[n - 1] == '0' || 
                num[n - 1] == '2' || 
                num[n - 1] == '4' || 
                num[n - 1] == '6' || 
                num[n - 1] == '8') 
				result = true
			end

		end

		if (result == true) 
			print(" Given number (", num ,") is divisible by 2", "\n")
		else
 
			print(" Given number (", num ,") is not divisible by 2", "\n")
		end

	end

end

def main() 
	task = Divisibility.new()
	#  Test
	task.isDivisibleBy2("122938934834534345345343940")
	task.isDivisibleBy2("2342348234")
	task.isDivisibleBy2("2398231234233251")
	task.isDivisibleBy2("33282949823493")
end

main()

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2

import scala.collection.mutable._;
// Scala program for
// Check that if large number is divisible by 2
class Divisibility()
{
	def isDivisibleBy2(num: String): Unit = {
		// Condition
		// ➀ Last digit should be a Even number
		var result: Boolean = false;
		var n: Int = num.length();
		if (n == 1 && num.charAt(0) == '0')
		{
			// Given number is zero
			result = true;
		}
		else if (n > 0)
		{
			if (num.charAt(n - 1) == '0' || 
                num.charAt(n - 1) == '2' || 
                num.charAt(n - 1) == '4' || 
                num.charAt(n - 1) == '6' || 
                num.charAt(n - 1) == '8')
			{
				result = true;
			}
		}
		if (result == true)
		{
			println(" Given number (" + num + ") is divisible by 2");
		}
		else
		{
			println(" Given number (" + num + ") is not divisible by 2");
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Divisibility = new Divisibility();
		// Test
		task.isDivisibleBy2("122938934834534345345343940");
		task.isDivisibleBy2("2342348234");
		task.isDivisibleBy2("2398231234233251");
		task.isDivisibleBy2("33282949823493");
	}
}

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2
import Foundation;
// Swift 4 program for
// Check that if large number is divisible by 2
class Divisibility
{
	func isDivisibleBy2(_ n: String)
	{
      	let num = Array(n);
		// Condition
		// ➀ Last digit should be a Even number
		var result: Bool = false;
		let n: Int = num.count;
		if (n == 1 && num[0] == "0")
		{
			// Given number is zero
			result = true;
		}
		else if (n > 0)
		{
			if (num[n - 1] == "0" || 
                num[n - 1] == "2" || 
                num[n - 1] == "4" || 
                num[n - 1] == "6" || 
                num[n - 1] == "8")
			{
				result = true;
			}
		}
		if (result == true)
		{
			print(" Given number (", n ,") is divisible by 2");
		}
		else
		{
			print(" Given number (", n ,") is not divisible by 2");
		}
	}
}
func main()
{
	let task: Divisibility = Divisibility();
	// Test
	task.isDivisibleBy2("122938934834534345345343940");
	task.isDivisibleBy2("2342348234");
	task.isDivisibleBy2("2398231234233251");
	task.isDivisibleBy2("33282949823493");
}
main();

Output

 Given number ( 27 ) is divisible by 2
 Given number ( 10 ) is divisible by 2
 Given number ( 16 ) is not divisible by 2
 Given number ( 14 ) is not divisible by 2
// Kotlin program for
// Check that if large number is divisible by 2
class Divisibility
{
	fun isDivisibleBy2(num: String): Unit
	{
		// Condition
		// ➀ Last digit should be a Even number
		var result: Boolean = false;
		val n: Int = num.length;
		if (n == 1 && num.get(0) == '0')
		{
			// Given number is zero
			result = true;
		}
		else if (n > 0)
		{
			if (num.get(n - 1) == '0' || 
                num.get(n - 1) == '2' || 
                num.get(n - 1) == '4' || 
                num.get(n - 1) == '6' || 
                num.get(n - 1) == '8')
			{
				result = true;
			}
		}
		if (result == true)
		{
			println(" Given number (" + num + ") is divisible by 2");
		}
		else
		{
			println(" Given number (" + num + ") is not divisible by 2");
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: Divisibility = Divisibility();
	// Test
	task.isDivisibleBy2("122938934834534345345343940");
	task.isDivisibleBy2("2342348234");
	task.isDivisibleBy2("2398231234233251");
	task.isDivisibleBy2("33282949823493");
}

Output

 Given number (122938934834534345345343940) is divisible by 2
 Given number (2342348234) is divisible by 2
 Given number (2398231234233251) is not divisible by 2
 Given number (33282949823493) is not divisible by 2

Resultant Output Explanation

The provided Java code implements the above algorithm. It checks the last digit of the given number and verifies if it is even. Based on the result, it prints whether the number is divisible by 2 or not.

Time Complexity

The time complexity of this code is O(1) because it only involves checking the last digit of the given number, which can be done in constant time regardless of the number's length.

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