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Code Mathematics

# Check divisibility by 7 without modulus operator

This problem is solved in two ways, one basic method uses addition and subtraction operations.

``````// C program for
// Check divisibility by 7 without modulus operator
#include <stdio.h>

// This is check that given number is divisible by 7 or not
void divisibleBy7(int number)
{
int num = number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
printf(" Number %d is divisible by 7\n", number);
}
else
{
// When it's not divisible by 7
printf(" Number %d is not divisible by 7\n", number);
}
}
int main(int argc, char
const *argv[])
{
// Test Case
divisibleBy7(-21);
divisibleBy7(-26);
divisibleBy7(21);
divisibleBy7(326);
divisibleBy7(7315);
return 0;
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````/*
Java Program for
Check divisibility by 7 without modulus operator
*/
public class Divisibility
{
// This is check that given number is divisible by 7 or not
public void divisibleBy7(int number)
{
int num = number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
System.out.println(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
System.out.println(" Number " + number + " is not divisible by 7");
}
}
public static void main(String[] args)
{
// Test Case
}
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````// Include header file
#include <iostream>
using namespace std;

/*
C++ Program for
Check divisibility by 7 without modulus operator
*/

class Divisibility
{
public:
// This is check that given number is divisible by 7 or not
void divisibleBy7(int number)
{
int num = number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
cout << " Number " << number << " is divisible by 7" << endl;
}
else
{
// When it's not divisible by 7
cout << " Number " << number << " is not divisible by 7" << endl;
}
}
};
int main()
{
// Test Case
return 0;
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````// Include namespace system
using System;
/*
Csharp Program for
Check divisibility by 7 without modulus operator
*/
public class Divisibility
{
// This is check that given number is divisible by 7 or not
public void divisibleBy7(int number)
{
int num = number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
Console.WriteLine(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
Console.WriteLine(" Number " + number + " is not divisible by 7");
}
}
public static void Main(String[] args)
{
// Test Case
}
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````<?php
/*
Php Program for
Check divisibility by 7 without modulus operator
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
public	function divisibleBy7(\$number)
{
\$num = \$number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (\$num <= -7 || \$num >= 7)
{
if (\$num <= -7)
{
// When number is negative and less than -6
\$num += 7;
}
else
{
// Reduce the number by -7
\$num -= 7;
}
}
if (\$num == 0)
{
// When it's divisible by 7
echo " Number ".\$number.
" is divisible by 7".
"\n";
}
else
{
// When it's not divisible by 7
echo " Number ".\$number.
" is not divisible by 7".
"\n";
}
}
}

function main()
{
// Test Case
}
main();``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````/*
Node JS Program for
Check divisibility by 7 without modulus operator
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
divisibleBy7(number)
{
var num = number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
console.log(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
console.log(" Number " + number + " is not divisible by 7");
}
}
}

function main()
{
// Test Case
}
main();``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````#  Python 3 Program for
#  Check divisibility by 7 without modulus operator
class Divisibility :
#  This is check that given number is divisible by 7 or not
def divisibleBy7(self, number) :
num = number
#  Execute the loop until,
#  When number is outside the range of (-7 to 7)
while (num <= -7 or num >= 7) :
if (num <= -7) :
#  When number is negative and less than -6
num += 7
else :
#  Reduce the number by -7
num -= 7

if (num == 0) :
#  When it's divisible by 7
print(" Number ", number ," is divisible by 7")
else :
#  When it's not divisible by 7
print(" Number ", number ," is not divisible by 7")

def main() :
#  Test Case

if __name__ == "__main__": main()``````

#### input

`````` Number  -21  is divisible by 7
Number  -26  is not divisible by 7
Number  21  is divisible by 7
Number  326  is not divisible by 7
Number  7315  is divisible by 7``````
``````#  Ruby Program for
#  Check divisibility by 7 without modulus operator
class Divisibility
#  This is check that given number is divisible by 7 or not
def divisibleBy7(number)
num = number
#  Execute the loop until,
#  When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
if (num <= -7)
#  When number is negative and less than -6
num += 7
else
#  Reduce the number by -7
num -= 7
end

end

if (num == 0)
#  When it's divisible by 7
print(" Number ", number ," is divisible by 7", "\n")
else
#  When it's not divisible by 7
print(" Number ", number ," is not divisible by 7", "\n")
end

end

end

def main()
#  Test Case
end

main()``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7
``````
``````/*
Scala Program for
Check divisibility by 7 without modulus operator
*/
class Divisibility()
{
// This is check that given number is divisible by 7 or not
def divisibleBy7(number: Int): Unit = {
var num: Int = number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
println(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
println(" Number " + number + " is not divisible by 7");
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Divisibility = new Divisibility();
// Test Case
}
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````/*
Swift 4 Program for
Check divisibility by 7 without modulus operator
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
func divisibleBy7(_ number: Int)
{
var num: Int = number;
// Execute the loop until,
// When number is outside the range of (-7 to 7)
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
print(" Number ", number ," is divisible by 7");
}
else
{
// When it's not divisible by 7
print(" Number ", number ," is not divisible by 7");
}
}
}
func main()
{
// Test Case
}
main();``````

#### input

`````` Number  -21  is divisible by 7
Number  -26  is not divisible by 7
Number  21  is divisible by 7
Number  326  is not divisible by 7
Number  7315  is divisible by 7``````
``````/*
Kotlin Program for
Check divisibility by 7 without modulus operator
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
fun divisibleBy7(number: Int): Unit
{
var num: Int = number;
while (num <= -7 || num >= 7)
{
if (num <= -7)
{
// When number is negative and less than -6
num += 7;
}
else
{
// Reduce the number by -7
num -= 7;
}
}
if (num == 0)
{
// When it's divisible by 7
println(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
println(" Number " + number + " is not divisible by 7");
}
}
}
fun main(args: Array < String > ): Unit
{
// Test Case
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````

Time complexity of above program is n. We can reduce this complexity. See next solution.

The problem of checking whether a number is divisible by 7 without using the modulus operator can be challenging but can be solved using a simple algorithm.

The modulus operator (%) returns the remainder when one number is divided by another. For example, 10 % 3 = 1, which means that 10 is not divisible by 3.

To check divisibility by 7, we can use the following algorithm:

2. Double the digit and subtract it from the remaining digits.
3. Repeat steps 1 and 2 with the new number.
4. If the result is divisible by 7, then the original number is also divisible by 7.

For example, let's check whether the number 378 is divisible by 7:

2. Double the digit and subtract it from the remaining digits: 37 - 2 * 8 = 21
3. Repeat steps 1 and 2 with the new number: 1
4. 1 is not divisible by 7, so 378 is not divisible by 7.

This algorithm works because multiplying a number by 2 is equivalent to shifting its binary representation one bit to the left. Therefore, subtracting the doubled digit is equivalent to subtracting a multiple of 7. If the resulting number is divisible by 7, then the original number is also divisible by 7.

``````// C program for
// Check divisibility by 7 without modulus operator
// Efficient solution
#include <stdio.h>

// This is check that given number is divisible by 7 or not
void divisibleBy7(int number)
{
int num = number;
if (num < 0)
{
// When number is negative then change in positive
num = -num;
}
// When num is greater than 6 continue execute loop
while (num >= 7)
{
if (num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 *10 ) get last digit (same as num % 10)
num = (num / 10) - (2 *(num - num / 10 *10));
}
}
if (num == 0)
{
// When it's divisible by 7
printf(" Number %d is divisible by 7\n", number);
}
else
{
// When it's not divisible by 7
printf(" Number %d is not divisible by 7\n", number);
}
}
int main(int argc, char
const *argv[])
{
// Test Case
divisibleBy7(-21);
divisibleBy7(-26);
divisibleBy7(21);
divisibleBy7(326);
divisibleBy7(7315);
return 0;
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````/*
Java Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/

public class Divisibility
{
// This is check that given number is divisible by 7 or not
public void divisibleBy7(int number)
{
int num = number;

if(num < 0)
{
// When number is negative then change in positive
num = -num;
}
// When num is greater than 6 continue execute loop
while ( num >= 7)
{
if(num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 * 10 ) get last digit (same as num % 10)
num =  (num / 10) - (2 * ( num - num / 10 * 10 ));
}
}
if (num == 0)
{
// When it's divisible by 7
System.out.println(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
System.out.println(" Number " + number + " is not divisible by 7");
}
}
public static void main(String[] args)
{

// Test Case

}
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````// Include header file
#include <iostream>
using namespace std;

/*
C++ Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/

class Divisibility
{
public:
// This is check that given number is divisible by 7 or not
void divisibleBy7(int number)
{
int num = number;
if (num < 0)
{
// When number is negative then change in positive
num = -num;
}
// When num is greater than 6 continue execute loop
while (num >= 7)
{
if (num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 *10 ) get last digit (same as num % 10)
num = (num / 10) - (2 *(num - num / 10 *10));
}
}
if (num == 0)
{
// When it's divisible by 7
cout << " Number " << number << " is divisible by 7" << endl;
}
else
{
// When it's not divisible by 7
cout << " Number " << number << " is not divisible by 7" << endl;
}
}
};
int main()
{
// Test Case
return 0;
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````// Include namespace system
using System;
/*
Csharp Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/
public class Divisibility
{
// This is check that given number is divisible by 7 or not
public void divisibleBy7(int number)
{
int num = number;
if (num < 0)
{
// When number is negative then change in positive
num = -num;
}
// When num is greater than 6 continue execute loop
while (num >= 7)
{
if (num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 * 10 ) get last digit (same as num % 10)
num = (num / 10) - (2 * (num - num / 10 * 10));
}
}
if (num == 0)
{
// When it's divisible by 7
Console.WriteLine(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
Console.WriteLine(" Number " + number + " is not divisible by 7");
}
}
public static void Main(String[] args)
{
// Test Case
}
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````<?php
/*
Php Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
public	function divisibleBy7(\$number)
{
\$num = \$number;
if (\$num < 0)
{
// When number is negative then change in positive
\$num = -\$num;
}
// When num is greater than 6 continue execute loop
while (\$num >= 7)
{
if (\$num < 10)
{
// Reduce of the number by -7
\$num = \$num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 * 10 ) get last digit (same as num % 10)
\$num = ((int)(\$num / 10)) - (2 * (\$num - (int)(\$num / 10) * 10));
}
}
if (\$num == 0)
{
// When it's divisible by 7
echo " Number ".\$number.
" is divisible by 7".
"\n";
}
else
{
// When it's not divisible by 7
echo " Number ".\$number.
" is not divisible by 7".
"\n";
}
}
}

function main()
{
// Test Case
}
main();``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````/*
Node JS Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
divisibleBy7(number)
{
var num = number;
if (num < 0)
{
// When number is negative then change in positive
num = -num;
}
// When num is greater than 6 continue execute loop
while (num >= 7)
{
if (num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 * 10 ) get last digit (same as num % 10)
num = (parseInt(num / 10)) - (2 * (num - parseInt(num / 10) * 10));
}
}
if (num == 0)
{
// When it's divisible by 7
console.log(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
console.log(" Number " + number + " is not divisible by 7");
}
}
}

function main()
{
// Test Case
}
main();``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````#  Python 3 Program for
#  Check divisibility by 7 without modulus operator
#  Efficient solution

class Divisibility :
#  This is check that given number is divisible by 7 or not
def divisibleBy7(self, number) :
num = number
if (num < 0) :
#  When number is negative then change in positive
num = -num

#  When num is greater than 6 continue execute loop
while (num >= 7) :
if (num < 10) :
#  Reduce of the number by -7
num = num - 7
else :
#  (num / 10) Remove last digit of a number
#  ( num - num / 10 * 10 ) get last digit (same as num % 10)
num = (int(num / 10)) - (2 * (num - int(num / 10) * 10))

if (num == 0) :
#  When it's divisible by 7
print(" Number ", number ," is divisible by 7")
else :
#  When it's not divisible by 7
print(" Number ", number ," is not divisible by 7")

def main() :
#  Test Case

if __name__ == "__main__": main()``````

#### input

`````` Number  -21  is divisible by 7
Number  -26  is not divisible by 7
Number  21  is divisible by 7
Number  326  is not divisible by 7
Number  7315  is divisible by 7``````
``````#  Ruby Program for
#  Check divisibility by 7 without modulus operator
#  Efficient solution

class Divisibility
#  This is check that given number is divisible by 7 or not
def divisibleBy7(number)
num = number
if (num < 0)
#  When number is negative then change in positive
num = -num
end

#  When num is greater than 6 continue execute loop
while (num >= 7)
if (num < 10)
#  Reduce of the number by -7
num = num - 7
else
#  (num / 10) Remove last digit of a number
#  ( num - num / 10 * 10 ) get last digit (same as num % 10)
num = (num / 10) - (2 * (num - num / 10 * 10))
end

end

if (num == 0)
#  When it's divisible by 7
print(" Number ", number ," is divisible by 7", "\n")
else
#  When it's not divisible by 7
print(" Number ", number ," is not divisible by 7", "\n")
end

end

end

def main()
#  Test Case
end

main()``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7
``````
``````/*
Scala Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/
class Divisibility()
{
// This is check that given number is divisible by 7 or not
def divisibleBy7(number: Int): Unit = {
var num: Int = number;
if (num < 0)
{
// When number is negative then change in positive
num = -num;
}
// When num is greater than 6 continue execute loop
while (num >= 7)
{
if (num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 * 10 ) get last digit (same as num % 10)
num = ((num / 10).toInt) - (2 * (num - (num / 10).toInt * 10));
}
}
if (num == 0)
{
// When it's divisible by 7
println(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
println(" Number " + number + " is not divisible by 7");
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Divisibility = new Divisibility();
// Test Case
}
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````
``````/*
Swift 4 Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
func divisibleBy7(_ number: Int)
{
var num: Int = number;
if (num < 0)
{
// When number is negative then change in positive
num = -num;
}
// When num is greater than 6 continue execute loop
while (num >= 7)
{
if (num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 * 10 ) get last digit (same as num % 10)
num = (num / 10) - (2 * (num - num / 10 * 10));
}
}
if (num == 0)
{
// When it's divisible by 7
print(" Number ", number ," is divisible by 7");
}
else
{
// When it's not divisible by 7
print(" Number ", number ," is not divisible by 7");
}
}
}
func main()
{
// Test Case
}
main();``````

#### input

`````` Number  -21  is divisible by 7
Number  -26  is not divisible by 7
Number  21  is divisible by 7
Number  326  is not divisible by 7
Number  7315  is divisible by 7``````
``````/*
Kotlin Program for
Check divisibility by 7 without modulus operator
Efficient solution
*/
class Divisibility
{
// This is check that given number is divisible by 7 or not
fun divisibleBy7(number: Int): Unit
{
var num: Int = number;
if (num < 0)
{
// When number is negative then change in positive
num = -num;
}
while (num >= 7)
{
if (num < 10)
{
// Reduce of the number by -7
num = num - 7;
}
else
{
// (num / 10) Remove last digit of a number
// ( num - num / 10 * 10 ) get last digit (same as num % 10)
num = (num / 10) - (2 * (num - num / 10 * 10));
}
}
if (num == 0)
{
// When it's divisible by 7
println(" Number " + number + " is divisible by 7");
}
else
{
// When it's not divisible by 7
println(" Number " + number + " is not divisible by 7");
}
}
}
fun main(args: Array < String > ): Unit
{
// Test Case
}``````

#### input

`````` Number -21 is divisible by 7
Number -26 is not divisible by 7
Number 21 is divisible by 7
Number 326 is not divisible by 7
Number 7315 is divisible by 7``````

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