f[n_] := f[n, Mod[n, 15]]
f[_, 0] := "FizzBuzz"

f[n_, _] := f[n, Mod[n, {3, 5}]]
f[_, {0, _}] := "Fizz"
f[_, {_, 0}] := "Buzz"
f[n_, {_, _}] := n

f /@ Range[100]