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Even numbers, because they are evenly divisible by 2, always return 0, while odd numbers always return the remainder of 1.Computer Architecture - COMPUTER-ARCHITECTURE This is possible because x % 2 always returns either 0 or 1. One of the most basic use cases for the modulus operator is to determine if a number is even or odd. I found it far more interesting as I started to learn its practical utility. When I first encountered the it, the modulus operator seemed little more than a bit of mathematical trivia. While returning the remainder is what the modulo operation does, that's not its only use indeed we'll see that it's handy for a good deal more - but that was a necessary starting point. For our purposes here, we'll only be dealing with positive integers. Some people find this abstract representation helps deepen or clarify their understanding of the operation, but you don't need to know it.Ī final note here - if you're wondering how the modulo operation functions with negative numbers or decimals, that's a bit outside the scope of this article. If you don't find the formula helpful, don't worry - I didn't either at first. The Modulo Operation Expressed As a FormulaĪs one final means of explication, for those more mathematically inclined, here's a formula that describes the modulo operation: a - (n * floor (a /n ) )īy substituting values, we can see how the modulo operation works in practice: 100 % 7 = 2 If this seems strange, boring, or not particularly useful, bear with me a bit longer - or just skip ahead to the use cases. That remainder is what the modulo operation returns. Mathematics with whole numbers behaves differently - when dividing numbers that aren't even multiples, there's always some amount left over. It may be helpful to think back to your early math lessons, before you learned fractions and decimals. 5 divided by 5 equals 1, with a remainder of 0 5 divided by 4 equals 1, with a remainder of 1 5 divided by 3 equals 1, with a remainder of 2 5 divided by 2 equals 2, with a remainder of 1 5 divided by 1 equals 5, with a remainder of 0 Some examples may help illustrate this, as it's not necessarily intuitive the first time you encounter it: 5 % 1 = 0 Instead of returning the result of the division, the modulo operation returns the whole number remainder. The modulus operator - or more precisely, the modulo operation - is a way to determine the remainder of a division operation. Rotating Through Limited Options (Circular Array).The Modulo Operation Expressed As a Formula.You next response, understandably, might be, 'That doesn't clarify anything,' so let's take a closer look: The modulus operator, written in most programming languages as % or mod, performs what is known as the modulo operation. I was not taught %, the modulus operator, which I recently discovered can be quite useful and interesting in its own right. These are the four mathematical operations I was taught during my childhood education, and their operators, +, -, *, /, are very familiar. Addition, subtraction, multiplication, and division.