$a=2^2\ast 3^3\ast 5\ast 7\ast 17,b=2^3\ast 3^2\ast 5\ast 11\ast 19$
НОД (a;b) = $2^2\ast 3^2\ast 5=4\ast 9\ast 5=20\ast 9=180$

$a=2^5\ast 3^2\ast 7^3\ast 13\ast {23}^2,b=3^5\ast 7\ast {13}^2\ast 23$
НОД (a;b) = $3^2\ast 7\ast 13\ast 23=9\ast 7\ast 13\ast 23=63\ast 13\ast 23=819\ast 23=18837$

Вычисления:
$\begin{array}{r}\times \underset{¯}{\begin{array}{r}63\\ 13\end{array}}\\ 189\\ 63\phantom{0}\\ \overline{819}\end{array}$
 
$\begin{array}{r}\times \underset{¯}{\begin{array}{r}819\\ 23\end{array}}\\ 2457\\ 1638\phantom{0}\\ \overline{18837}\end{array}$