[tex]folosim \: \: formula \: \: lui \: \: legendre : [/tex]
[tex] \nu_p(n!) = \sum_{i = 1}^ \infty [ \frac{n}{p^i}],[/tex]
[tex]cu \: \: {p}^{i} < n.[/tex]
[tex]calculam \: \: \nu_5.[/tex]
[tex] \nu_5 (53!) = [ \frac{53}{5} ] + [ \frac{53}{25} ] = [10.5] + [2.12] = 10 + 2 = 12[/tex]
