Modulus

The modulus operator is represented by the % symbol, and it gives us the remainder of a division operation.

For example, the remainder of 7 divided by 3 is 1, because 3 goes into 7 twice (which is 6), and there is 1 left over.

We can use the modulus operator like this:

int remainder = 7 % 3; // 1
int remainder2 = 10 % 4; // 2
int remainder3 = 15 % 5; // 0

Common use: odd/even checking

One of the most common uses for the % operator is to check whether a number is odd or even. An even number is divisible by 2 with no (0) remainder, whereas an odd number has a remainder of 1 when divided by 2.

So we could check for an even number like this:

int number = 8;
bool isEven = (number % 2 == 0); // true

…or for an odd number like this:

int number = 7;
bool isOdd = (number % 2 == 1); // true

Common use: wrapping values

Suppose we have a variable that represents a colour in the RGB format.

The last 8 bits of the RGB value represent the blue component, which can have a value from 0 to 255. We can get the last 8 bits by finding the remainder when dividing by 256 (because 256 is 2^8, or 1 followed by 8 zeroes in binary):

int rgbValue = 0xFFAA33; // some RGB colour value
int blueComponent = rgbValue % 256; // 0x33 (51 in decimal)

This technique of using the modulus operator to ‘wrap’ values around a certain range is very common in programming!

A case study: fizzbuzz

A classic programming exercise is called fizzbuzz. The task is to print the numbers from 1 to 100, but for multiples of 3, print "fizz" instead of the number, for multiples of 5, print "buzz" instead of the number, and for multiples of both 3 and 5, print "fizzbuzz" instead of the number.

Here is a (bad) implementation of fizzbuzz in C#:

for (int i = 1; i <= 100; i++)
{
    if (i % 3 == 0 && i % 5 == 0)
    {
        Console.WriteLine("fizzbuzz");
    }
    else if (i % 3 == 0)
    {
        Console.WriteLine("fizz");
    }
    else if (i % 5 == 0)
    {
        Console.WriteLine("buzz");
    }
    else
    {
        Console.WriteLine(i);
    }
}

Don’t worry if you don’t understand all of this code yet. It covers concepts that we haven’t covered yet, such as loops and conditional statements. The key parts are the modulus operations (i % 3 and i % 5), which check whether i is a multiple of 3 or 5.

There are far better ways to implement fizzbuzz - e.g. by building up a string, or using a hashmap (or Dictionary in C#) - but this basic implementation shows the uses of the modulus operator.