Let's optimize the if statements away, too (no extra memory accesses or branches, either).

  #include <stdio.h>
  #include <stdint.h>
  
  #define F(n) (1 << (2*(n)-2))
  #define B(n) (1 << (2*(n)-1))
  
  int main() {
    uint32_t m = F(3) | F(6) | F(9) | F(12) | F(15) | B(5) | B(10) | B(15);
    int i;
    static char t[4][16]= { "%d\n", "Fizz\n", "Buzz\n", "FizzBuzz\n" };
    for (i = 1; i <= 100; i++) {
      printf(t[m&3], i);
      m = (m >> 2) | (m << 28);
    }
    return 0;
  }

Transforming that into an if-based version is left as an exercise for the reader. :)