If $p$ is a prime number,then $n^p - n$ is divisible by $p$ when $n$ is a

The number of natural number solutions to the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to

The number of positive odd divisors of $216$ is

Consider the following statements:
$I$: The number of non-trivial even divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $(\alpha_1+2\alpha_3+\alpha_5)(\alpha_2+\alpha_5+1)(\alpha_4+1)-1$.
$II$: The number of non-trivial odd divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $\alpha_2+\alpha_4+\alpha_5+\alpha_2\alpha_4+\alpha_4\alpha_5$. Then:

The exponent of $6$ in $72!$ is

The number of positive integers $n$ such that $n+3$ divides $n^3-3$ is