Question

Let $y$ be the product of all the divisors of the number $720$ . If $y$ is divisible by $15^{p},$ then maximum value of $\left(\frac{p}{3}\right)$ equals

Answer 1

$720=2^{4}\times 3^{2}\times 5^{1}$
Total number of cases

Similarly $3$ more cases with powers $2^{3}, \, 2^{4}, \, 2^{0}.$
Power of $3=5\times \left(2 + 4\right)=30$
Power of $5=5\times 3=15$
$15^{P}=5^{P}\times 3^{P}$
Max. value of $P=15$