% John David Stone
% Department of Mathematics and Computer Science
% Grinnell College
% stone@cs.grinnell.edu

% created June 19, 2002
% last revised June 19, 2002

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\begin{document}
\textbf{Algorithm E} (\textit{Euclid's algorithm}).  Given two positive
integers $m$ and $n$, find their \textit{greatest common divisor}, that is,
the largest positive integer that evenly divides both $m$ and $n$.

\begin{itemize}
\item[\textbf E1.] [Find remainder.]  Divide $m$ by $n$ and let $r$ be the
remainder. (We will have $0 \le r < n$.)
\item[\textbf E2.] [Is it zero?]  If $r = 0$, the algorithm terminates; $n$
is the answer.
\item[\textbf E3.] [Reduce.]  Set $m \leftarrow n$, $n \leftarrow r$, and
go back to step 1. \quad \rule[-0.5 ex]{0.5 ex}{1.75 ex}
\end{itemize}
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