Find all numbers that have 30 factors and have 30 as one of their factors. Find all numbers that have 30 factors and have 30 as one of their factors.
Thank you. 
Note: please show way if possible.

We write the  number as $2^{1+a}3^{1+b}{5^{1+c}}n$ with $(n,30)=1$. 
The number of divisors of the number is $30=(2+a)(2+b)(2+c)\tau(n)$. Hence $\tau(n)=1\implies n=1$ ($\tau(n)$ is the number of divisors of $n$).
So $2+a,2+b,2+c$ are $2,3,5$ in some order.
There are $6$ solutions:
$2\cdot3^2\cdot5^4=11250$
$2\cdot3^4\cdot5^2=4050$
$2^2\cdot3\cdot5^4=7500$
$2^2\cdot3^4\cdot5=1620$
$2^4\cdot3\cdot5^2=1200$
$2^4\cdot3^2\cdot5=720$
