Modulo Operation/Examples/100 mod 3

Theorem

 * $100 \bmod 3 = 1$

where $\bmod$ denotes the modulo operation.

Proof
By definition of modulo operation:
 * $x \bmod y := x - y \left \lfloor {\dfrac x y}\right \rfloor$

for $y \ne 0$.

We have:
 * $\dfrac {100} 3 = 33 + \dfrac 1 3$

and so:
 * $\left\lfloor{\dfrac {100} 3}\right\rfloor = 33$

Thus: