Yes you can use Legendre Theorem here.
It states the highest power of a prime number "p" in N! would be = Σ[N/pk]. where k = 1,2,..... and [.] denotes greatest integer function.
For example the power of 5 in 100! would be [100/5] + [100/25] + [100/125] +.... = 20+4 = 24. ie 100! will have 5^24.
So in this case check the prime number, for which you get the exponent to be three or more.
Only 31 will satisy that condition.
Hence option (B) using Legendre Theorem !!.
Ashwin (IIT Madras).