How to find highest power of 56 that 433! is divided
I've tried to use that power is equals to 433/56, but it is obviously not enough
2026-04-06 19:31:07.1775503867
How to find highest power of 56
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Calculate $$\left\lfloor\frac{433}{7}\right\rfloor+\left\lfloor\frac{433}{7^2}\right\rfloor+\left\lfloor\frac{433}{7^3}\right\rfloor.$$ I got $70$.
Thus, it's enough to check that $433!$ is divisible by $2^{3\cdot70}$, which is obvious because $$\left\lfloor\frac{433}{2}\right\rfloor+\left\lfloor\frac{433}{2^2}\right\rfloor+...>210.$$ Id est, $433!$ is divisible by $56^{70}$ and $70$ is a maximal power.