Floor Division Calculator
Perform division with integer results, calculate quotients and remainders
Calculate Floor Division
The number being divided
The number to divide by (cannot be zero)
Division by Zero
Division by zero is undefined. Please enter a non-zero divisor.
Floor Division Formula
⌊a ÷ b⌋ = q
Floor of standard division
a = q × b + r
Division algorithm
a = dividend (number being divided)
b = divisor (number dividing by)
q = quotient (integer result)
r = remainder (what's left)
⌊⌋ = floor function (round down)
Key Concepts
Always Integer Result
Floor division always yields whole numbers
Round Down
Result is largest integer ≤ standard division
Remainder Included
Shows what's left after division
Negative Numbers
Floor function still applies (round down)
Quick Examples
⌊13 ÷ 4⌋ = 3
13 = 3 × 4 + 1
⌊26 ÷ 5⌋ = 5
26 = 5 × 5 + 1
⌊-7 ÷ 5⌋ = -2
-7 = -2 × 5 + 3
⌊20 ÷ 4⌋ = 5
20 = 5 × 4 + 0 (exact)
Understanding Floor Division
What is Floor Division?
Floor division, also known as integer division, is an operation that divides one number by another and rounds the result down to the nearest integer. Unlike regular division which can produce decimal results, floor division always returns a whole number.
How It Works:
1. Perform standard division (a ÷ b)
2. Apply the floor function ⌊⌋ (round down)
3. Calculate remainder using: r = a - (q × b)
4. Verify: a = q × b + r
Key Differences
Regular Division
35 ÷ 4 = 8.75 (decimal result)
Floor Division
⌊35 ÷ 4⌋ = 8 (integer result)
Applications
• Distributing items equally
• Calculating required containers/groups
• Programming algorithms
• Time calculations (hours, minutes)
• Resource allocation problems
Special Cases
Negative Numbers
When dealing with negative numbers, the floor function still rounds down to the next smaller integer.
⌊-7 ÷ 5⌋ = ⌊-1.4⌋ = -2
-7 = -2 × 5 + 3
Exact Division
When the dividend is perfectly divisible by the divisor, the remainder is zero.
⌊20 ÷ 4⌋ = ⌊5⌋ = 5
20 = 5 × 4 + 0
Programming Context
Floor division is widely used in programming for array indexing, pagination, time calculations, and algorithms. Different programming languages provide various ways to perform floor division:
Python
a // b
JavaScript
Math.floor(a / b)
Java/C/C++
a / b (integers)