Mathematics

Check that if large number is divisible by 18

The problem involves checking whether a given large number is divisible by 18. To determine if a number is divisible by 18, we need to ensure that it satisfies two conditions: it should be divisible by 2 and divisible by 9.

Problem Statement

Given a large number as a string, the task is to check if the number is divisible by 18.

Idea to Solve the Problem

To solve this problem, we can follow these steps:

Check if the last digit of the number is even (0, 2, 4, 6, 8). If it is, then the number is divisible by 2.
Calculate the sum of all the digits in the number. If the sum is divisible by 9, then the number is divisible by 9.
If both conditions from steps 1 and 2 are satisfied, then the number is divisible by 18.

Pseudocode

class Divisibility
    method isDivisibleBy18(num)
        result = false
        n = length of num
        if n == 1 and num.charAt(0) == '0'
            result = true
        else if n > 1
            if last digit of num is even
                sum = 0
                for i from 0 to n - 1
                    sum += (num.charAt(i) - 48)
                if sum % 9 == 0
                    result = true
        if result is true
            print "Given number (" + num + ") is divisible by 18"
        else
            print "Given number (" + num + ") is not divisible by 18"

function main
    task = new Divisibility
    task.isDivisibleBy18("34534564565")
    task.isDivisibleBy18("32473248726872398347612")
    task.isDivisibleBy18("234234242")
    task.isDivisibleBy18("565678678435345353465475654626")

Algorithm Explanation

The isDivisibleBy18 method checks if a given large number (as a string) is divisible by 18:

If the number is 0, it is divisible by 18, so we set result to true.
If the last digit of the number is even, we calculate the sum of its digits and check if the sum is divisible by 9.
If both conditions are satisfied, we set result to true.

The main function tests the method with different large numbers.

Program solution

// Java program for
// Check that if large number is divisible by 18
public class Divisibility
{
	public void isDivisibleBy18(String num)
	{
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		boolean result = false;
		int n = num.length();
		if (n == 1 && num.charAt(0) == '0')
		{
			// When given number is zero
			result = true;
		}
		else if (n > 1)
		{
			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')
			{
				// Number is divisible by 2
				int sum = 0;
				// Calculate sum of all digit
				for (int i = 0; i < n; ++i)
				{
					sum += (num.charAt(i) - 48);
				}
				if ((sum % 9) == 0)
				{
					// When number divisible by 9
					result = true;
				}
			}
		}
		if (result == true)
		{
			System.out.print(" Given number (" + 
                             num + ") is divisible by 18\n");
		}
		else
		{
			System.out.print(" Given number (" + 
                             num + ") is not divisible by 18\n");
		}
	}
	public static void main(String[] args)
	{
		Divisibility task = new Divisibility();
		// Test
		task.isDivisibleBy18("34534564565");
		task.isDivisibleBy18("32473248726872398347612");
		task.isDivisibleBy18("234234242");
		task.isDivisibleBy18("565678678435345353465475654626");
	}
}

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

// Include header file
#include <iostream>
#include <string>

using namespace std;
// C++ program for
// Check that if large number is divisible by 18
class Divisibility
{
	public: void isDivisibleBy18(string num)
	{
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		bool result = false;
		int n = num.length();
		if (n == 1 && num[0] == '0')
		{
			// When given number is zero
			result = true;
		}
		else if (n > 1)
		{
			if (num[n - 1] == '0' || 
                num[n - 1] == '2' || 
                num[n - 1] == '4' || 
                num[n - 1] == '6' || 
                num[n - 1] == '8')
			{
				// Number is divisible by 2
				int sum = 0;
				// Calculate sum of all digit
				for (int i = 0; i < n; ++i)
				{
					sum += (num[i] - 48);
				}
				if ((sum % 9) == 0)
				{
					// When number divisible by 9
					result = true;
				}
			}
		}
		if (result == true)
		{
			cout << " Given number (" 
                 << num << ") is divisible by 18\n";
		}
		else
		{
			cout << " Given number (" 
                 << num << ") is not divisible by 18\n";
		}
	}
};
int main()
{
	Divisibility *task = new Divisibility();
	// Test
	task->isDivisibleBy18("34534564565");
	task->isDivisibleBy18("32473248726872398347612");
	task->isDivisibleBy18("234234242");
	task->isDivisibleBy18("565678678435345353465475654626");
	return 0;
}

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

// Include namespace system
using System;
// Csharp program for
// Check that if large number is divisible by 18
public class Divisibility
{
	public void isDivisibleBy18(String num)
	{
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		Boolean result = false;
		int n = num.Length;
		if (n == 1 && num[0] == '0')
		{
			// When given number is zero
			result = true;
		}
		else if (n > 1)
		{
			if (num[n - 1] == '0' || 
                num[n - 1] == '2' || 
                num[n - 1] == '4' || 
                num[n - 1] == '6' || 
                num[n - 1] == '8')
			{
				// Number is divisible by 2
				int sum = 0;
				// Calculate sum of all digit
				for (int i = 0; i < n; ++i)
				{
					sum += (num[i] - 48);
				}
				if ((sum % 9) == 0)
				{
					// When number divisible by 9
					result = true;
				}
			}
		}
		if (result == true)
		{
			Console.Write(" Given number (" + num + ") is divisible by 18\n");
		}
		else
		{
			Console.Write(" Given number (" + num + ") is not divisible by 18\n");
		}
	}
	public static void Main(String[] args)
	{
		Divisibility task = new Divisibility();
		// Test
		task.isDivisibleBy18("34534564565");
		task.isDivisibleBy18("32473248726872398347612");
		task.isDivisibleBy18("234234242");
		task.isDivisibleBy18("565678678435345353465475654626");
	}
}

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

package main
import "fmt"
// Go program for
// Check that if large number is divisible by 18
type Divisibility struct {}
func getDivisibility() * Divisibility {
	var me *Divisibility = &Divisibility {}
	return me
}
func(this Divisibility) isDivisibleBy18(num string) {
	// Condition
	// ➀  Number should be divisible by 2
	// ➁  Number should be divisible by 9
	var result bool = false
	var n int = len(num)
	if n == 1 && num[0] == '0' {
		// When given number is zero
		result = true
	} else if n > 1 {
		if num[n - 1] == '0' || num[n - 1] == '2' || 
		   num[n - 1] == '4' || num[n - 1] == '6' || 
		   num[n - 1] == '8' {
			// Number is divisible by 2
			var sum int = 0
			// Calculate sum of all digit
			for i := 0 ; i < n ; i++ {
				sum += (int(num[i]) - 48)
			}
			if (sum % 9) == 0 {
				// When number divisible by 9
				result = true
			}
		}
	}
	if result == true {
		fmt.Print(" Given number (", 
			num, ") is divisible by 18\n")
	} else {
		fmt.Print(" Given number (", 
			num, ") is not divisible by 18\n")
	}
}
func main() {
	var task * Divisibility = getDivisibility()
	// Test
	task.isDivisibleBy18("34534564565")
	task.isDivisibleBy18("32473248726872398347612")
	task.isDivisibleBy18("234234242")
	task.isDivisibleBy18("565678678435345353465475654626")
}

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

<?php
// Php program for
// Check that if large number is divisible by 18
class Divisibility
{
	public	function isDivisibleBy18($num)
	{
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		$result = false;
		$n = strlen($num);
		if ($n == 1 && $num[0] == '0')
		{
			// When given number is zero
			$result = true;
		}
		else if ($n > 1)
		{
			if ($num[$n - 1] == '0' || 
                $num[$n - 1] == '2' || 
                $num[$n - 1] == '4' || 
                $num[$n - 1] == '6' || 
                $num[$n - 1] == '8')
			{
				// Number is divisible by 2
				$sum = 0;
				// Calculate sum of all digit
				for ($i = 0; $i < $n; ++$i)
				{
					$sum += (ord($num[$i]) - 48);
				}
				if (($sum % 9) == 0)
				{
					// When number divisible by 9
					$result = true;
				}
			}
		}
		if ($result == true)
		{
			echo(" Given number (".$num.
				") is divisible by 18\n");
		}
		else
		{
			echo(" Given number (".$num.
				") is not divisible by 18\n");
		}
	}
}

function main()
{
	$task = new Divisibility();
	// Test
	$task->isDivisibleBy18("34534564565");
	$task->isDivisibleBy18("32473248726872398347612");
	$task->isDivisibleBy18("234234242");
	$task->isDivisibleBy18("565678678435345353465475654626");
}
main();

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

// Node JS program for
// Check that if large number is divisible by 18
class Divisibility
{
	isDivisibleBy18(num)
	{
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		var result = false;
		var n = num.length;
		if (n == 1 && num.charAt(0) == '0')
		{
			// When given number is zero
			result = true;
		}
		else if (n > 1)
		{
			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')
			{
				// Number is divisible by 2
				var sum = 0;
				// Calculate sum of all digit
				for (var i = 0; i < n; ++i)
				{
					sum += (num.charAt(i).charCodeAt(0) - 48);
				}
				if ((sum % 9) == 0)
				{
					// When number divisible by 9
					result = true;
				}
			}
		}
		if (result == true)
		{
			process.stdout.write(" Given number (" + num + ") is divisible by 18\n");
		}
		else
		{
			process.stdout.write(" Given number (" + num + ") is not divisible by 18\n");
		}
	}
}

function main()
{
	var task = new Divisibility();
	// Test
	task.isDivisibleBy18("34534564565");
	task.isDivisibleBy18("32473248726872398347612");
	task.isDivisibleBy18("234234242");
	task.isDivisibleBy18("565678678435345353465475654626");
}
main();

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

#  Python 3 program for
#  Check that if large number is divisible by 18
class Divisibility :
	def isDivisibleBy18(self, num) :
		#  Condition
		#  ➀  Number should be divisible by 2
		#  ➁  Number should be divisible by 9
		result = False
		n = len(num)
		if (n == 1 and num[0] == '0') :
			#  When given number is zero
			result = True
		elif (n > 1) :
			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') :
				#  Number is divisible by 2
				sum = 0
				i = 0
				#  Calculate sum of all digit
				while (i < n) :
					sum += (ord(num[i]) - 48)
					i += 1
				
				if ((sum % 9) == 0) :
					#  When number divisible by 9
					result = True
				
			
		
		if (result == True) :
			print(" Given number (", num ,") is divisible by 18")
		else :
			print(" Given number (", num ,") is not divisible by 18")
		
	

def main() :
	task = Divisibility()
	#  Test
	task.isDivisibleBy18("34534564565")
	task.isDivisibleBy18("32473248726872398347612")
	task.isDivisibleBy18("234234242")
	task.isDivisibleBy18("565678678435345353465475654626")

if __name__ == "__main__": main()

Output

 Given number ( 34534564565 ) is not divisible by 18
 Given number ( 32473248726872398347612 ) is divisible by 18
 Given number ( 234234242 ) is not divisible by 18
 Given number ( 565678678435345353465475654626 ) is divisible by 18

#  Ruby program for
#  Check that if large number is divisible by 18
class Divisibility 
	def isDivisibleBy18(num) 
		#  Condition
		#  ➀  Number should be divisible by 2
		#  ➁  Number should be divisible by 9
		result = false
		n = num.length
		if (n == 1 && num[0] == '0') 
			#  When given number is zero
			result = true
		elsif (n > 1) 
			if (num[n - 1] == '0' || 
                num[n - 1] == '2' || 
                num[n - 1] == '4' || 
                num[n - 1] == '6' || 
                num[n - 1] == '8') 
				#  Number is divisible by 2
				sum = 0
				i = 0
				#  Calculate sum of all digit
				while (i < n) 
					sum += (num[i].ord - 48)
					i += 1
				end

				if ((sum % 9) == 0) 
					#  When number divisible by 9
					result = true
				end

			end

		end

		if (result == true) 
			print(" Given number (", num ,") is divisible by 18\n")
		else
 
			print(" Given number (", num ,") is not divisible by 18\n")
		end

	end

end

def main() 
	task = Divisibility.new()
	#  Test
	task.isDivisibleBy18("34534564565")
	task.isDivisibleBy18("32473248726872398347612")
	task.isDivisibleBy18("234234242")
	task.isDivisibleBy18("565678678435345353465475654626")
end

main()

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

import scala.collection.mutable._;
// Scala program for
// Check that if large number is divisible by 18
class Divisibility()
{
	def isDivisibleBy18(num: String): Unit = {
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		var result: Boolean = false;
		var n: Int = num.length();
		if (n == 1 && num.charAt(0) == '0')
		{
			// When given number is zero
			result = true;
		}
		else if (n > 1)
		{
			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')
			{
				// Number is divisible by 2
				var sum: Int = 0;
				var i: Int = 0;
				// Calculate sum of all digit
				while (i < n)
				{
					sum += (num.charAt(i).toInt - 48);
					i += 1;
				}
				if ((sum % 9) == 0)
				{
					// When number divisible by 9
					result = true;
				}
			}
		}
		if (result == true)
		{
			print(" Given number (" + num + ") is divisible by 18\n");
		}
		else
		{
			print(" Given number (" + num + ") is not divisible by 18\n");
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Divisibility = new Divisibility();
		// Test
		task.isDivisibleBy18("34534564565");
		task.isDivisibleBy18("32473248726872398347612");
		task.isDivisibleBy18("234234242");
		task.isDivisibleBy18("565678678435345353465475654626");
	}
}

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

import Foundation;
// Swift 4 program for
// Check that if large number is divisible by 18
class Divisibility
{
	func isDivisibleBy18(_ v: String)
	{
      	let num = Array(v);
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		var result: Bool = false;
		let n: Int = num.count;
		if (n == 1 && num[0] == "0")
		{
			// When given number is zero
			result = true;
		}
		else if (n > 1)
		{
			if (num[n - 1] == "0" || 
                num[n - 1] == "2" || 
                num[n - 1] == "4" || 
                num[n - 1] == "6" || 
                num[n - 1] == "8")
			{
				// Number is divisible by 2
				var sum: Int = 0;
				var i: Int = 0;
				// Calculate sum of all digit
				while (i < n)
				{
					sum += (Int(UnicodeScalar(String(num[i]))!.value) - 48);
					i += 1;
				}
				if ((sum % 9) == 0)
				{
					// When number divisible by 9
					result = true;
				}
			}
		}
		if (result == true)
		{
			print(" Given number (", v ,") is divisible by 18");
		}
		else
		{
			print(" Given number (", v ,") is not divisible by 18");
		}
	}
}
func main()
{
	let task: Divisibility = Divisibility();
	// Test
	task.isDivisibleBy18("34534564565");
	task.isDivisibleBy18("32473248726872398347612");
	task.isDivisibleBy18("234234242");
	task.isDivisibleBy18("565678678435345353465475654626");
}
main();

Output

 Given number ( 34534564565 ) is not divisible by 18
 Given number ( 32473248726872398347612 ) is divisible by 18
 Given number ( 234234242 ) is not divisible by 18
 Given number ( 565678678435345353465475654626 ) is divisible by 18

// Kotlin program for
// Check that if large number is divisible by 18
class Divisibility
{
	fun isDivisibleBy18(num: String): Unit
	{
		// Condition
		// ➀  Number should be divisible by 2
		// ➁  Number should be divisible by 9
		var result: Boolean = false;
		val n: Int = num.length;
		if (n == 1 && num.get(0) == '0')
		{
			// When given number is zero
			result = true;
		}
		else if (n > 1)
		{
			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')
			{
				// Number is divisible by 2
				var sum: Int = 0;
				var i: Int = 0;
				// Calculate sum of all digit
				while (i < n)
				{
					sum += (num.get(i).toInt() - 48);
					i += 1;
				}
				if ((sum % 9) == 0)
				{
					// When number divisible by 9
					result = true;
				}
			}
		}
		if (result == true)
		{
			print(" Given number (" + num + ") is divisible by 18\n");
		}
		else
		{
			print(" Given number (" + num + ") is not divisible by 18\n");
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: Divisibility = Divisibility();
	// Test
	task.isDivisibleBy18("34534564565");
	task.isDivisibleBy18("32473248726872398347612");
	task.isDivisibleBy18("234234242");
	task.isDivisibleBy18("565678678435345353465475654626");
}

Output

 Given number (34534564565) is not divisible by 18
 Given number (32473248726872398347612) is divisible by 18
 Given number (234234242) is not divisible by 18
 Given number (565678678435345353465475654626) is divisible by 18

Time Complexity

The time complexity of this algorithm is O(n), where n is the number of digits in the given large number.

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