Modulus Operator in C++

The modulus operator (%) in C++ returns the remainder of a division operation between two integers. It is commonly used in programming for tasks such as checking for even/odd numbers, cyclic operations, hashing, and modular arithmetic.

Syntax

result = dividend % divisor;

• Both operands must be integers (e.g., int, long, short, etc.).
• The result is the remainder when dividend is divided by divisor.

1. Basic Usage of Modulus

int a = 10, b = 3;
int result = a % b;
std::cout << "Result: " << result;  // Output: 1

In the example above:

• 10 / 3 gives 3 with a remainder of 1
• So, 10 % 3 = 1

2. Division vs Modulus

int a = 17, b = 5;
std::cout << "Division: " << a / b << std::endl; // 3
std::cout << "Modulus: " << a % b << std::endl;  // 2

• a / b gives the quotient
• a % b gives the remainder

3. Modulus with Negative Numbers

Behavior of % with negative numbers is defined by the C++ standard:

int a = -17, b = 5;
std::cout << "-17 % 5 = " << a % b << std::endl;  // Output: -2
 
a = 17, b = -5;
std::cout << "17 % -5 = " << a % b << std::endl;  // Output: 2
 
a = -17, b = -5;
std::cout << "-17 % -5 = " << a % b << std::endl; // Output: -2

The sign of the result follows the sign of the dividend (left-hand operand).

4. Modulus with char and ASCII

Characters are treated as integers via their ASCII values.

char a = 'A'; // ASCII 65
int result = a % 10;
std::cout << "Result: " << result;  // Output: 5

5. Floating-Point and Modulus

The % operator does not work with float or double. Attempting this causes a compile-time error.

// float a = 5.5f, b = 2.0f;
// float result = a % b;  // ❌ Compile-time error

For floating-point modulus, use the standard library function fmod():

#include <cmath>
 
double result = std::fmod(5.5, 2.0);
std::cout << "Result: " << result;  // Output: 1.5

6. Common Use Cases

Check Even or Odd

int n = 7;
if (n % 2 == 0)
    std::cout << "Even";
else
    std::cout << "Odd";

Find Last Digit of a Number

int num = 983;
int lastDigit = num % 10;
std::cout << "Last Digit: " << lastDigit;  // Output: 3

Circular Array or Loop Indexing

int index = (8 + 1) % 5;
std::cout << "Next Index: " << index;  // Output: 4

7. Modulus Operator in Expressions

int result = (5 + 3 * 2) % 4;
std::cout << "Result: " << result;  // Output: 3

Here’s how it’s evaluated:

• 3 * 2 = 6
• 5 + 6 = 11
• 11 % 4 = 3

8. Practice Problems

Problem 1: Remainder Without Using %

int a = 25, b = 4;
int remainder = a - (a / b) * b;
std::cout << "Remainder: " << remainder;  // Output: 1

Problem 2: Sum of Digits

int n = 1234, sum = 0;
while (n > 0) {
    sum += n % 10;
    n = n / 10;
}
std::cout << "Sum of digits: " << sum;  // Output: 10

Problem 3: Last Digit Equality

int a = 123, b = 993;
if (a % 10 == b % 10)
    std::cout << "Last digits match!";
else
    std::cout << "Different last digits.";

Summary Table

Best Practices

• Only use % with integers unless using fmod() for floating-point types.
• Be careful with negative numbers; remember the remainder follows the dividend’s sign.
• Always check for zero in denominator to avoid runtime errors.
• Use modulus to simplify cyclical patterns, such as rotating through an array or checking digit patterns.