\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
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In the Euclidean algorithm, if the Euclidean division of \(a\) by \(b\) is \(a = bq + r\), then we have:
\(\gcd(a, b) = \gcd(q, r)\)
\(\gcd(a, b) = \gcd(a, r)\)
\(\gcd(a, b) = \gcd(b, r)\)
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