The largest $\mathrm{n} \in \mathrm{N}$ such that $3^{\mathrm{n}}$ divides 50 ! is:

Question

Aicharya · Accepted Answer

$2^\alpha \cdot 3^\beta \cdot 5^\gamma$
$\mathrm{B}=\left[\frac{50}{3}\right]+\left[\frac{50}{3^2}\right]+\left[\frac{50}{3^3}\right]+\left[\frac{50}{3^4}\right]$
$=16+5+1=22$
Maximum value of $n$ is 22 /

The largest $\mathrm{n} \in \mathrm{N}$ such that $3^{\mathrm{n}}$ divides 50 ! is:

Solution