If $\alpha$ and $\beta$ are the greatest common divisors of $n(n^2-1)$ and $2n(n^2+2)$ respectively for all $n \in N$, then $\alpha \beta=$

The number of divisors of $9600$ including $1$ and $9600$ are

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

The sum of the divisors of $2^5 \times 3^4 \times 5^2$ is

The arithmetic mean of five natural numbers is $40$. The largest exceeds the smallest number by $10$. If $\alpha$ is the maximum possible value for the largest of these $5$ numbers,then the number of positive integral divisors of $\alpha$ is

The number of divisors of $7!$ is