Problem:
Find the greatest common divisor of $\{76,-381,-881\}$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the greatest common divisor}: \\
 \gcd (76,-381,-881) \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{Any }\text{divisor }\text{of }\text{a }\text{negative }\text{number }\text{is }\text{also }\text{a }\text{divisor }\text{of }\text{its }\text{absolute }\text{value}: \\
 \gcd (76,-381,-881)=\gcd (76,381,881) \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{l}
 \text{Find }\text{the }\text{divisors }\text{of }\text{each }\text{integer }\text{and }\text{select }\text{the }\text{largest }\text{element }\text{they }\text{have }\text{in }\text{common}: \\
 \text{The }\text{divisors }\text{of }\text{76 }\text{are}: \\
\end{array}
 \\
 1,2,4,19,38,76 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{The }\text{divisors }\text{of }\text{381 }\text{are}: \\
 1,3,127,381 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{The }\text{divisors }\text{of }\text{881 }\text{are}: \\
 1,881 \\
\end{array}
 \\
 
\begin{array}{l}
 
\begin{array}{l}
 \text{The }\text{largest }\text{number }\text{common }\text{to }\text{all }\text{divisor }\text{lists }\text{is }1: \\
 \text{divisors }\text{of }\text{76: }1,2,4,19,38,76 \\
 \text{divisors }\text{of }\text{381: }1,3,127,381 \\
 \text{divisors }\text{of }\text{881: }1,881 \\
\end{array}
 \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \gcd (76,-381,-881)=1 \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/gcd_w_steps/169.txt'}