Conform formulei lui Legendre,
produsul primelor 25 de numere naturale nenule se termină în:
[tex]\\\displaystyle \sum\limits_{k=1}^{\infty}\left[\dfrac{25}{5^k}\right] = \left[\dfrac{25}{5^1}\right]+\left[\dfrac{25}{5^2}\right]+\left[\dfrac{25}{5^3}\right]+... =\\\\\\ = \left[\dfrac{25}{5}\right]+\left[\dfrac{25}{25}\right]+\left[\dfrac{25}{125}\right]+... =\\ \\\\ = [5]+[1]+[0,2]+... = 5+1+0+... =\\\\ \\ = \boxed{6}\,\text{ zerouri.}[/tex]
