# 5.1: Floor division and modulus

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The floor division operator, //, divides two numbers and rounds down to an integer. For example, suppose the run time of a movie is 105 minutes. You might want to know how long that is in hours. Conventional division returns a floating-point number:

>>> minutes = 105
>>> minutes / 60
1.75


But we don’t normally write hours with decimal points. Floor division returns the integer number of hours, rounding down:

>>> minutes = 105
>>> hours = minutes // 60
>>> hours
1


To get the remainder, you could subtract off one hour in minutes:

>>> remainder = minutes - hours * 60
>>> remainder
45


An alternative is to use the modulus operator, %, which divides two numbers and returns the remainder.

>>> remainder = minutes % 60
>>> remainder
45


The modulus operator is more useful than it seems. For example, you can check whether one number is divisible by another—if x % y is zero, then x is divisible by y.

Also, you can extract the right-most digit or digits from a number. For example, x % 10 yields the right-most digit of x (in base 10). Similarly x % 100 yields the last two digits.

If you are using Python 2, division works differently. The division operator, /, performs floor division if both operands are integers, and floating-point division if either operand is a float.

This page titled 5.1: Floor division and modulus is shared under a CC BY-NC 3.0 license and was authored, remixed, and/or curated by Allen B. Downey (Green Tea Press) .