--- title: 3.12 Modulus Operator description: "The **modulus operator (`%`)** returns the **remainder** after dividing one number by another. Unlike the division operator (`/`), which returns the quotient, the modulus operator tells you what is left over after the division. The modulus operator is commonly used…" url: "https://edcret.in/docs/python-programming/numeric-data-types-python/3-12-modulus-operator/" updated: "2026-07-29" category: Python Programming / Numeric Data Types --- # 3.12 Modulus Operator The **modulus operator (`%`)** returns the **remainder** after dividing one number by another. Unlike the division operator (`/`), which returns the quotient, the modulus operator tells you what is left over after the division. The modulus operator is commonly used for checking whether a number is even or odd, finding cyclic patterns, validating input, and determining if one number is divisible by another. --- ## Syntax ``` result = dividend % divisor ``` ### Components | Component | Description | | --- | --- | | `dividend` | The number to be divided. | | `%` | Modulus operator. | | `divisor` | The number that divides the dividend. | | `result` | The remainder after division. | --- ## Example 1: Finding the Remainder **main.py** ``` print(17 % 5) ``` ### Output ``` 2 ``` ### Explanation - `17 ÷ 5` gives a quotient of `3` with a remainder of `2`. - The modulus operator returns the remainder. - Therefore, the result is `2`. --- ## Example 2: Exact Division **main.py** ``` print(20 % 4) ``` ### Output ``` 0 ``` ### Explanation - `20` is exactly divisible by `4`. - No remainder is left after the division. - Therefore, the result is `0`. --- ## Example 3: Checking Even or Odd **main.py** ``` number = 17 print(number % 2) ``` ### Output ``` 1 ``` ### Explanation - Dividing `17` by `2` leaves a remainder of `1`. - A remainder of `1` indicates an odd number. - A remainder of `0` indicates an even number. --- ## Example 4: Modulus with Floating-Point Numbers **main.py** ``` print(10.5 % 3) ``` ### Output ``` 1.5 ``` ### Explanation - The modulus operator also works with floating-point numbers. - `10.5 ÷ 3` leaves a remainder of `1.5`. - Python returns the floating-point remainder. --- ## Example 5: Negative Dividend **main.py** ``` print(-17 % 5) ``` ### Output ``` 3 ``` ### Explanation - Python's modulus operator follows floor division. - The result has the same sign as the divisor. - Therefore, `-17 % 5` evaluates to `3`. --- ## Example 6: Negative Divisor **main.py** ``` print(17 % -5) ``` ### Output ``` -3 ``` ### Explanation - The divisor is negative. - The remainder also has the sign of the divisor. - Therefore, the result is `-3`. --- ## Example 7: User Input **main.py** ``` number = int(input("Enter a number: ")) print(number % 2) ``` ### Sample Input ``` 24 ``` ### Output ``` 0 ``` ### Explanation - The user enters an integer. - The modulus operator calculates the remainder after division by `2`. - Since the remainder is `0`, the number is even. --- ## Example 8: Finding the Last Digit **main.py** ``` number = 5387 print(number % 10) ``` ### Output ``` 7 ``` ### Explanation - Dividing by `10` leaves the last digit as the remainder. - Therefore, the last digit of `5387` is `7`. --- ## Example 9: Using Modulus in an Expression **main.py** ``` result = (15 + 8) % 6 print(result) ``` ### Output ``` 5 ``` ### Explanation - First, `15 + 8` equals `23`. - Then `23 % 6` is calculated. - The remainder is `5`. --- ## Example 10: Checking the Return Type **main.py** ``` print(type(17 % 5)) print(type(17.5 % 5)) ``` ### Output ``` ``` ### Explanation - When both operands are integers, the result is an integer. - If either operand is a floating-point number, the result is a float. --- # Common Mistakes ### 1. Confusing Modulus with Division **Incorrect** ``` print(15 % 4) ``` ### Incorrect Expectation ``` 3.75 ``` ### Actual Output ``` 3 ``` **Reason** The modulus operator returns the remainder, not the quotient. --- ### 2. Assuming Negative Results Behave Like Other Languages **Incorrect** ``` print(-10 % 3) ``` ### Incorrect Expectation ``` -1 ``` ### Actual Output ``` 2 ``` **Reason** Python calculates the remainder based on floor division. The remainder has the same sign as the divisor. --- ### 3. Dividing by Zero **Incorrect** ``` print(10 % 0) ``` ### Output ``` ZeroDivisionError: integer modulo by zero ``` **Reason** The divisor cannot be zero. --- ### 4. Expecting the Original Variable to Change **Incorrect** ``` number = 19 number % 5 print(number) ``` ### Output ``` 19 ``` **Reason** The modulus operator returns a new value. It does not modify the original variable. **Correct** ``` number = number % 5 print(number) ``` --- # Best Practices - Use `%` to determine whether a number is divisible by another number. - Use `% 2` when checking whether a number is even or odd. - Remember that the remainder follows Python's floor division rules for negative numbers. - Ensure the divisor is not zero before using the modulus operator. - Store the result if it will be reused later. --- # Key Points to Remember - `%` is the modulus operator in Python. - It returns the remainder after division. - If the remainder is `0`, the dividend is exactly divisible by the divisor. - The modulus operator works with integers and floating-point numbers. - The remainder follows Python's floor division rules and has the same sign as the divisor. - Dividing or taking the modulus by zero raises a `ZeroDivisionError`. - The modulus operator is commonly used for checking divisibility, even/odd numbers, and extracting digits.