2. If $1 \times 2 \times \cdots \times 100=12^{n} M$, where $M$ is a natural number, and $n$ is the largest natural number that makes the equation true, then $M$ ( ).
(A) is divisible by 2 but not by 3
(B) is divisible by 3 but not by 2
(C) is divisible by 4 but not by 3
(D) is not divisible by 3, nor by 2
(1991, National Junior High School Mathematics League)
(Tip: In the prime factorization of 100!, the exponent of 2 is 97, and the exponent of 3 is 48. Let $100!=2^{97} \times 3^{48} \times M_{1}=12^{18} \times 2 M_{1}$. Choose (A).)