Question

How many trialling zeros in 214!

Answer 1

$\huge\star{\tt{\underline{\underline{\red{Answer}}}}}\star$

For zeroes in 214!

6.

#Zero can be only obtained by 2 and 5

So,

Expo of 2 in 214! = $\bigg[\frac{214}{2}\bigg]$ + $\bigg[\frac{214}{4}\bigg]$+$\bigg[\frac{214}{8}\bigg]$ +$\bigg[\frac{214}{16}\bigg]$+$\bigg[\frac{214}{32}\bigg]$ + $\bigg[\frac{214}{64}\bigg]$. +$\bigg[\frac{214}{128}\bigg]$+ $\bigg[\frac{214}{256}\bigg]$

Note: [.] is G.I.F

$\implies$ [107] + [ 53.5] + [26.75] + [13.1] + [6. ] + [3. ] + [1. ] + [0]

$\implies$ 107+53+26+13+6+3+1+0

$\implies$ $\huge{\boxed{\boxed{206\: zeroes\: in\: 214!}}}$