The number of positive divisors of $1080$ is

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

The greatest integer $r$ such that $30^{r}$ divides $30!$ is

Let $N$ be the least positive integer such that whenever a non-zero digit $c \in \{1, 2, \dots, 9\}$ is written after the last digit of $N$,the resulting number is divisible by $c$. The sum of the digits of $N$ is:

The coefficient of $a^{3} b^{4} c^{5}$ in the expansion of $(bc + ca + ab)^{6}$ is

The number of positive integral solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{2025}$ is