AHSME 1974 Problem 26

The number of distinct positive integral divisors of $(30)^4$ excluding $1$ and $(30)^4$ is $\mathrm{(A)\ } 100 \mathrm{(B) \ }125 \mathrm{(C) \ } 123 \mathrm{(D) \ } 30 \mathrm{(E) \ }\text{none of these}$