Question

Find the number of zeroes at the end of $300 !$.

Answer 1

$E _{2}=(300 !)$
$=\left[\frac{300}{2}\right]+\left[\frac{300}{2^{2}}\right]+\left[\frac{300}{2^{3}}\right]+\left[\frac{300}{2^{4}}\right]+\left[\frac{300}{2^{5}}\right]+{\left[\frac{300}{2^{6}}\right]+\left[\frac{300}{2^{7}}\right]+\left[\frac{300}{2^{8}}\right]+\ldots }$
$E _{2}(300 !)=150+75+37+18+9+4+2+1$
$=296$
$E _{5}(300 !)=\left[\frac{300}{5}\right]+\left[\frac{300}{5^{2}}\right]+\left[\frac{300}{5^{3}}\right]+\ldots \ldots . .$
$=60+12+2=74$
No. of zeroes $=74$