jmc

We prime factorize the given number as $2^8\cdot 3^2\cdot 5^4$. A factor of this number takes the form $2^a{3}^b{5}^c$ for integers $a$ between 0 and 8, $b$ between 0 and 2, and $c$ between 0 and 4. There are $9$ ways to choose $a$, 3 ways to choose $b$, and 5 ways to choose $c$. In total, there are $9\cdot 3\cdot 5=\boxed{135}$ factors.