+197 \(8=2^3.\)
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
