# How to generalize it?

Number Theory Level 4

Find the largest non-negative integer $$n$$ such that $$2^n$$ is a factor $\left\lfloor\sqrt2\right\rfloor\times\left\lfloor\sqrt3\right\rfloor\times\left\lfloor\sqrt4\right\rfloor\times\cdots\times\left\lfloor\sqrt{99}\right\rfloor$

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