The number of zeros at the end of $100!$ is

Let $f(x) = 2x^n + \lambda$,where $\lambda \in R$ and $n \in N$. Given $f(4) = 133$ and $f(5) = 255$,find the sum of all the positive integer divisors of $(f(3) - f(2))$.

The smallest positive divisor greater than $1$ of a composite number $a$ is

The number of positive integers $n$ in the set $\{2, 3, \ldots, 200\}$ such that $\frac{1}{n}$ has a terminating decimal expansion is

If $1000! = 3^n \times m$ where $m$ is an integer not divisible by $3$, then $n = $

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