1. What is Floor Division?

Floor division is a mathematical operation that divides two numbers and returns the largest integer less than or equal to the result. In Python, it's represented by the // operator.

2. How Does Floor Division Work?

The floor division operation:

Where:

• \( a \) — Dividend (numerator)
• \( b \) — Divisor (denominator)
• \( \lfloor \rfloor \) — Floor function notation

Explanation: Floor division always rounds down to the nearest integer, even for negative numbers.

3. Python Floor Division Examples

Examples:

• 7 // 2 = 3 (regular division is 3.5)
• -7 // 2 = -4 (regular division is -3.5)
• 10.5 // 3 = 3.0 (regular division is 3.5)

4. Using the Calculator

Tips: Enter any two numbers (integers or decimals). The calculator will compute the floor division result. Division by zero is not allowed.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between / and // in Python?
A: / performs regular division (returns float), while // performs floor division (returns integer or float depending on inputs).

Q2: How does floor division work with negative numbers?
A: It still rounds down (toward negative infinity), so -7 // 2 gives -4 (not -3).

Q3: Can I use floor division with floating point numbers?
A: Yes, but the result will be a float that's mathematically equal to an integer (e.g., 5.0 instead of 5).

Q4: What's the relationship between floor division and modulo?
A: In Python, (a // b) * b + (a % b) == a for all numbers where b != 0.

Q5: When should I use floor division?
A: When you need integer division that rounds down, like splitting items into equal groups where you can't have fractions.