How Does Modulus Divison Work

I don't really understand how modulus division works. I was calculating 27 % 16 and wound up with 11 and I don't understand why.

I can't seem to find an explanation in layman's terms online. Can someone elaborate on a very high level as to what's going on here?

Solution 1:

Most explanations miss one important step, let's fill the gap using another example.

Given the following:

Dividend: 16
Divisor: 6

The modulus function looks like this:

16 % 6 = 4

Let's determine why this is.

First, perform integer division, which is similar to normal division, except any fractional number (a.k.a. remainder) is discarded:

16 / 6 = 2

Then, multiply the result of the above division (2) with our divisor (6):

2 * 6 = 12

Finally, subtract the result of the above multiplication (12) from our dividend (16):

16 - 12 = 4

The result of this subtraction, 4, the remainder, is the same result of our modulus above!

The result of a modulo division is the remainder of an integer division of the given numbers.

That means:

27 / 16 = 1, remainder 11
=> 27 mod 16 = 11

Other examples:

30 / 3 = 10, remainder 0
=> 30 mod 3 = 0

35 / 3 = 11, remainder 2
=> 35 mod 3 = 2