Modulo Operation/Examples/100 mod 7

Theorem

 * $100 \bmod 7 = 2$

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:
 * $\dfrac {100} 7 = 14 + \dfrac 2 7$

and so:
 * $\left\lfloor{\dfrac {100} 7}\right\rfloor = 14$

Thus: