Question

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

Answer 1

Answer: 74.00

$E_2=(300!)$
$=\left[\frac{300}{2}\right]+\left[\frac{300}{2^2}\right]+\left[\frac{300}{2^3}\right]+\left[\frac{300}{2^4}\right]+\left[\frac{300}{2^5}\right]+\left[\frac{300}{2^6}\right]+\left[\frac{300}{2^7}\right]+\left[\frac{300}{2^8}\right]+\dots$
$E_2(300!)=150+75+37+18+9+4+2+1$
$=296$
$E_5(300!)=\left[\frac{300}{5}\right]+\left[\frac{300}{5^2}\right]+\left[\frac{300}{5^3}\right]+\dots \dots ..$
$=60+12+2=74$
No. of zeroes $=74$