12. Find the largest natural number $n$ which satisfies the inequality
$$
n^{6033}<2011^{2011} \text {. }
$$
12. Answer: 12
Since $6033=3 \times 2011$, we have
$$
\begin{aligned}
n^{6003}2011$. Thus, the largest possible natural number $n$ satisfying the given inequality is 12 .