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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Example 10: Checking the Return Type #

main.py

print(type(17 % 5))
print(type(17.5 % 5))

Output #

<class 'int'>
<class 'float'>

Explanation #

• When both operands are integers, the result is an integer.
• If either operand is a floating-point number, the result is a float.

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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.

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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.

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3. Dividing by Zero #

Incorrect

print(10 % 0)

Output #

ZeroDivisionError: integer modulo by zero

Reason

The divisor cannot be zero.

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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)

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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.

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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.