Question

What is the largest power of $12$ that would divide $49!$

Answer 1

To check the highest power of $12$ in $49!$ we need to check the highest powers of $4$ and $3$ in it
Highest power of $3$ in $49!=22$
Highest power of $2$ in $49!=46$
$\therefore$ Highest power of $4$ in $49!=$$\frac{46}{2}=23$
$\therefore$ Highest power of $12$ will be $22$ (Since the common power between $3$ and $4$ is $22$)