4. For any positive integers $n$ and $k(k \leqslant n)$, let $f(n, k)$ denote the number of positive integers not exceeding $\left[\frac{n}{k}\right]$ that are coprime with $n$ (where $[x]$ denotes the greatest integer not exceeding $x$), then $f(100,3)=$
A. 11
B. 13
C. 14
D. 19
$f(100,3)$ represents the number of positive integers not exceeding $\left[\frac{100}{3}\right]=33$ and coprime with 100. Since $100=2^{2} \cdot 5^{2}$, the number of positive integers from $1 \sim 33$ that contain the factors 2, 5 is $\left[\frac{33}{2}\right]+\left[\frac{33}{5}\right]-\left[\frac{33}{10}\right]=16+6-3=19$. Therefore, the number of positive integers from $1 \sim 33$ that are coprime with 100 is $33-19=14$. So the answer is $C$.