smc

The prime factorization of $30$ is $2\cdot 3\cdot 5$, so the prime factorization of $30^4$ is $2^4\cdot 3^4\cdot 5^4$. Therefore, the number of positive divisors of $30^4$ is $(4+1)(4+1)(4+1)=125$. However, we have to subtract $2$ to account for $1$ and $30^4$, so our final answer is $ 125-2=123, \boxed{123} soln by RNVAA