Floor Division in Python is performed using the // (double forward slash) operator. Unlike regular division (/), floor division always rounds down the result to the nearest whole number (integer), regardless of whether the numbers are positive or negative.
The modulo operator % in Python is closely related to floor division. The identity a = (a // b) * b + (a % b) always holds true, which is Python's equivalent of Euclid's Division Lemma.
The // operator divides the left number by the right number and then floors the result — meaning it rounds down to the nearest integer.
# Regular division
print(7 / 2) # Output: 3.5
# Floor division
print(7 // 2) # Output: 3 (rounds DOWN from 3.5)
print(10 // 3) # Output: 3 (10/3 = 3.33... → rounds to 3)
print(15 // 4) # Output: 3 (15/4 = 3.75 → rounds to 3)
This is where floor division behaves differently from simple truncation. For negative numbers, 'rounding down' means going further away from zero (toward more negative values).
print(-7 // 2) # Output: -4 (NOT -3!)
# -7/2 = -3.5 → floor rounds DOWN to -4
print(7 // -2) # Output: -4
# 7/-2 = -3.5 → floor rounds DOWN to -4
print(-7 // -2) # Output: 3
# -7/-2 = +3.5 → floor rounds DOWN to 3
`/` is true division — it always returns a `float` (e.g., 7/2 = 3.5). `//` is floor division — it returns the largest integer ≤ the true result (e.g., 7//2 = 3). If both operands are integers, `//` returns an int; if either is a float, it returns a float.
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