\ANG{
K"urze mit Hilfe der Kettendivision:\qquad 
(a)\quad $\D\frac{313937}{230299}$\qquad
(b) $\D\frac{149379}{159681}$\quad 

}
\LSG{
\begin{enumerate}
\item \rule{0mm}{0mm}
\vspace{-14mm}

\begin{alignat*}{4}
 313937\,&:\,230299 &&= 1\,&&\text{Rest}\,83638 &&\\
 230299\,&:83638\, &&= 2\,&&\text{Rest}\,63023 &&\\
 83638\,&:\,63023 &&= 1\,&&\text{Rest}\,20615 &&\\
 63023\,&:\,20615 &&= 3\,&&\text{Rest}\,1178 &&\\
 20615\,&:\,1178 &&= 17\,&&\text{Rest}\,589 &&\\
 1178\,&:\,\boxed{589} &&= 2\,&&\text{Rest}\,0 &&\quad\DANN\quad 
   \ggT(313937,\,230299)=\underline{\underline{589}}
\end{alignat*}
\[\frac{313937}{230299}=\frac{313937\,:\,589}{230299\,:\,589}=\frac{533}{391}\]


\item \rule{0mm}{0mm}
\vspace{-14mm}

\begin{alignat*}{4}
 159681\,&:\,149379 &&= 1\,&&\text{Rest}\,10302 &&\\
 149379\,&:\,10302 &&= 14\,&&\text{Rest}\,5151 &&\\
 10302\,&:\,\boxed{5151} &&= 2\,&&\text{Rest}\,0 &&\quad\DANN\quad 
   \ggT(159681,\,149379)=\underline{\underline{5151}}
\end{alignat*}
\[\frac{149379}{159681}=\frac{149379\,:\,5151}{159681\,:\,5151}=\frac{31}{29}\]
\end{enumerate}
}



