4. For any positive integers $n$ and $k(k \leqslant n)$, $f(n, k)$ represents the number of positive integers not exceeding $\left[\frac{n}{k}\right]$ (where $[x]$ denotes the greatest integer not exceeding the real number $x$) that are coprime with $n$. Then $f(100,3)=(\quad)$.
(A) 11
(B) 13
(C) 14
(D) 19
4. C.

From $\left[\frac{100}{3}\right]=33$, we know that the required number is the count of numbers from 1 to 33 that are coprime with 100.

First, remove all even numbers, leaving 17 odd numbers. Then, remove multiples of 5 (a total of three), thus, the required number is 14.