Floor Division in Python

Division Operators allow you to divide two numbers and return a quotient, i.e., the first number or number at the left is divided by the second number or number at the right and returns the quotient. This article will explain how to execute floor division in Python.

What is Floor Division?

Floor division is a division operation that returns the largest integer that is less than or equal to the result of the division. In Python, it is denoted by the double forward slash ‘//’.

Example

If we divide 7 by 3 using floor division, we get:

2

Methods to perform Floor Division

• Using the Double Forward Slash Operator (//)
• Using the math.floor() Function

Using the Double Forward Slash Operator (//)

Syntax: result = dividend // divisor

Floor Division with Integers

In the code below, we have performed floor division between two integers In result1 we are performing floor division between two integers, 10 and 3. The result of dividing 10 by 3 is 3.333…., but floor division returns the largest integer less than or equal to the result. Therefore, the result is 3.

Python3

result1 = 10 // 3  # Result: 3

print("Floor division of two integers :", result1)

Output

Floor division of two integers : 3

Floor Division with Floating Numbers

In the code below, we have performed floor division between a floating number and an integer. In result2, we are performing floor division between a float (7.5) and an integer (2). The result of dividing 7.5 by 2 is 3.75, but floor division truncates the fractional part, resulting in 3.0.

Python3

result2 = 7.5 // 2
print("Floor division of a float and an integer :",result2)

Output

Floor division of a float and an integer : 3.0

Floor Division with Negative Integers

In the code below, we have performed floor division between two negative integers. In result3, we have floor division between a negative dividend (-17) and a negative divisor (-5). The result of dividing -17 by -5 is 3.4, but floor division returns the largest integer less than or equal to the result. Therefore, the result is 3.

Python3

result3 = -17 // -5
print("Floor division of two negative integers :",result3)

Output

Floor division of two negative integers : 3

Floor Division with Negative Integer and Positive Integer

In the code below, we have performed floor division between a positive and negative integer. In result4, we are performing floor division between two negative numbers, -17 and 5. The result of dividing -17 by 5 is -3.4, but floor division returns the largest integer less than or equal to the result. Therefore, the result is -4.

Python3

result4 = -17 // 5
print("Floor division with a negative dividend and positive divisor :", result4)

Output

Floor division with a negative dividend and positive divisor : -4

Using the math.floor() Function

math.floor() Division with Integers

In result, we are performing floor division between a float (7.5) and an integer (2). The result of dividing 7.5 by 2 is 3.75, but floor division truncates the fractional part, resulting in 3.0.

Python3

import math
result = math.floor(10 / 3)
print(result)

Output

3

math.floor() Division with Negative Integers

This code uses math.floor() to round down the result of -10 / 3, and it prints the rounded-down integer value, which is -4.

Python3

import math
result = math.floor(-10 / 3)
print(result)

Output

-4

Difference between Division and Floor Division

The division operator / performs standard division, which can result in a floating-point number (a decimal). If both the dividend and divisor are integers, Python will perform integer division if the result is an integer; otherwise, it will produce a floating-point result.

Python3

# Division Operator
result5 = 10/3
print(result5)

Output

3.3333333333333335

Whereas the floor division operator // performs division and returns the largest integer that is less than or equal to the division result. It truncates (rounds down) the fractional part of the result, ensuring that the result is always an integer.

Python3

# Floor Division
result6 = 10 // 3
print(result6)

Output

3