KöMaL 2019 K618

A positive integer $n$ is said to be a ``strong'' number if its number of divisors is greater than the number of divisors of each positive integer less than $n$. (For example, $n=2$ is a strong number, because it has two divisors, while $n=1$ has only one. But $n=3$ is not a strong number, because it has two divisors similarly to a smaller integer $n=2$.) $a)$ Find all strong numbers greater than 2 but less than 30. $b)$ Is $2^3\cdot3^4\cdot5$ a strong number?