How Does Modulus Divison Work

The simple formula for calculating modulus is :-

[Dividend-{(Dividend/Divisor)*Divisor}]

So, 27 % 16 :-

27- {(27/16)*16}

27-{1*16}

Answer= 11

Note:

All calculations are with integers. In case of a decimal quotient, the part after the decimal is to be ignored/truncated.

eg: 27/16= 1.6875 is to be taken as just 1 in the above mentioned formula. 0.6875 is ignored.

Compilers of computer languages treat an integer with decimal part the same way (by truncating after the decimal) as well

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

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!