NumTheSL5#3

$8=2^3.$

Thus, we have $\left \lfloor \frac{100}{2} \right \rfloor+\left \lfloor \frac{100}{4} \right \rfloor+...+\left \lfloor \frac{100}{32} \right \rfloor+\left \lfloor \frac{100}{64} \right \rfloor=97$. Since $97=32*3+1$, $\boxed{32}$ is our searched answer.

-azsun