The largest natural number $n$ such that $3^{n}$ divides $66!$ is $............$.

The number of proper divisors of the number obtained by dividing $13!$ by $100$ is

The coefficient of $x^{1012}$ in the expansion of $(1 + x^n + x^{253})^{10}$,where $n \leq 22$ is any positive integer,is

The coefficient of $x^{10}$ in the expansion of $(x+\frac{2}{x}-5)^{12}$ is

Among the positive divisors of the number $12600$,if $n_1$ is the number of divisors which are multiples of $3$ and $n_2$ is the number of divisors which are multiples of $14$,then $n_1 + n_2 =$

Let $d(n)$ denote the number of divisors of $n$ including $1$ and itself. Then, $d(225)$, $d(1125)$, and $d(640)$ are