The number of distinct positive integral divisors of excluding and is
Problem 32
Pick one
Official solution
(Error compiling LaTeX. Unknown error_msg)The prime factorization of $30$ is $2\cdot3\cdot5$, so the prime factorization of $30^4$ is $2^4\cdot3^4\cdot5^4$. 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{\text{C}}