Editing Floor and ceiling functions (section)

===Factors of factorials===
Let ''n'' be a positive integer and ''p'' a positive prime number. The exponent of the highest power of ''p'' that divides ''n''! is given by a version of [[Legendre's formula]]<ref>Hardy & Wright, Th. 416</ref>

:<math>\left\lfloor\frac{n}{p}\right\rfloor + \left\lfloor\frac{n}{p^2}\right\rfloor + \left\lfloor\frac{n}{p^3}\right\rfloor + \dots = \frac{n-\sum_{k}a_k}{p-1}</math>

where <math display="inline">n = \sum_{k}a_kp^k</math> is the way of writing ''n'' in base ''p''. This is a finite sum, since the floors are zero when ''p''<sup>''k''</sup> > ''n''.