Given two positive integers $n$ and $p$ where $p$ is prime and $p\leqslant n$ this calculator calculate the highest power $k$ of $p$ such that $p^k$ divide $n!$ evenly. The calculator find $k$ from the formula \[ k=\left\lfloor\dfrac{n}{p}\right\rfloor + \left\lfloor\dfrac{n}{p^2}\right\rfloor + \left\lfloor\dfrac{n}{p^3}\right\rfloor + \cdots \] where $\left\lfloor\frac{a}{b}\right\rfloor$ is the greatest integer that is less than or equal to $\frac{a}{b}$.

Reference

Carmichael, Robert D. The Theory of Numbers. 1914. pages 24-25. https://archive.org (Accessed 2015-11-11).

Prime Highest Power Calculator