Let $f$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ (where $\mathbb{R}$ is the set of all real numbers) that satisfies the following property: For every natural number $n$
$$f(n) = \text{the smallest prime factor of } n.$$
For example, $f(12) = 2$, $f(105) = 3$. Calculate the following.\\
(a) $\lim_{x \rightarrow \infty} f(x)$.\\
(b) The number of solutions to the equation $f(x) = 2016$.