How Does Modulus Divison Work

Question

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

Answer 1

Modulus division is pretty simple. It uses the remainder instead of the quotient.

    1.0833... <-- Quotient
   __
12|13
   12
    1 <-- Remainder
    1.00 <-- Remainder can be used to find decimal values
     .96
     .040
     .036
     .0040 <-- remainder of 4 starts repeating here, so the quotient is 1.083333...

13/12 = 1R1, ergo 13%12 = 1.

---

It helps to think of modulus as a "cycle".

In other words, for the expression n % 12, the result will always be < 12.

That means the sequence for the set 0..100 for n % 12 is:

{0,1,2,3,4,5,6,7,8,9,10,11,0,1,2,3,4,5,6,7,8,9,10,11,0,[...],4}

In that light, the modulus, as well as its uses, becomes much clearer.