1. What is Floor Division?

Floor division (also called integer division or quotient) divides two numbers and returns the largest integer less than or equal to the result. It effectively "rounds down" the division result to the nearest integer.

2. How Does the Calculator Work?

The calculator uses the floor division formula:

Where:

• \( a \) — Numerator (dividend)
• \( b \) — Denominator (divisor, cannot be zero)
• \( \left\lfloor x \right\rfloor \) — Floor function (greatest integer ≤ x)

Example: floor(7/3) = 2 (since 7÷3 ≈ 2.333, and floor rounds down to 2)

3. Importance of Floor Division

Applications: Floor division is essential in computer programming, discrete mathematics, and whenever you need whole number results from division (e.g., splitting items into boxes, calculating full weeks between dates).

4. Using the Calculator

Tips: Enter any real numbers for numerator and denominator (denominator cannot be zero). The calculator will return the integer quotient.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between floor division and regular division?
A: Regular division returns a float/decimal (7/3=2.333), while floor division returns an integer (7//3=2).

Q2: How is floor division different from ceiling division?
A: Floor rounds down (⌊3.7⌋=3), ceiling rounds up (⌈3.2⌉=4).

Q3: What happens with negative numbers?
A: Floor still rounds toward negative infinity (⌊-3.7⌋=-4).

Q4: Can I use zero as denominator?
A: No, division by zero is mathematically undefined.

Q5: How is this used in programming?
A: Many languages use "//" operator for floor division (Python) or have floor() functions.