$($a$)(2$ points$)$ Write the prime factorization of $GCD(2^5{3}^2{5}^{9}11,2^2{3}^7{7}^4).$

$($b$)(2$ points$)$ Write the prime factorization of LCM$(2^5{3}^2{5}^{9}11,2^2{3}^7{7}^4).$

$($c$)(2$ points$)$ How many factors of $2^5{3}^2{5}^{9}11$ are there? $($In other words, if

$x=2^5{3}^2{5}^{9}11,$ the problem asks you to calculate $\{$:$|\{kinN$:$k|x\}|).$