The exponent of $6$ in $72!$ is

To find the exponent of $6$ in $72!$ we will find exponent of $2 \& 3$,

So exponent of $2$ is given by,

$\left[\frac{72}{2}\right]+\left[\frac{72}{2^2}\right]+\left[\frac{72}{2^3}\right]+\left[\frac{72}{2^4}\right]+\left[\frac{72}{2^5}\right]+\left[\frac{72}{2^6}\right]$

$=36+18+9+4+2+1=66$

{where $\left[.\right]$ is greastest integer function}

Now finding the exponent of $3$ in $72!$ we get,

$\left[\frac{72}{3}\right]+\left[\frac{72}{3^2}\right]+\left[\frac{72}{3^3}\right]=24+8+2=34$

Now we know that $6=2\times 3$ so maximum power of $6$ we get depend upon exponent of $2 \& 3$

So we can see there is only $34$ exponent of $3$

So exponent of $6$ will be $34$.