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.

Let $n \in \mathbf N$. Writing the primefactor decomposition as 
$$ n = \prod_p p^{\alpha_p(n)}, $$
we know that $n$ has 
$$ \tau(n) = \prod_p \bigl(\alpha_p(n)+ 1\bigr) $$
divisors. (For any $p$ in a divisor we can choose $p$ appearing form $0$ to $\alpha_p(n)$ times), we have as $30 \mid n$, that $\alpha_p(n) \ge 1$, for $p \in \{2,3,5\}$. On the other hand, we must have that $2$, $3$ and $5$ appear in some $\alpha_p(n)+1$, as three of them are greater or equal to two, these must equal $2$, $3$ and $5$. So we are left with six possibilities
$$ 2^1 3^2 5^4, 2^1 3^4 5^2, 2^2 3^1 5^4, 2^2 3^4 5^1, 2^4 3^1 5^2, 2^4 3^2 5^1 $$
