Perform and visualise Euclidean algorithm on a pair of integers

euclideanAlgorithm.m

euclideanAlgorithmList[a_Integer, b_Integer] := NestWhileList[
  With[{newSortedPair = {Max@# - Floor[Max@#/Min@#] Min@#, Min@#}},
    If[#[[1]] > #[[2]], newSortedPair, Reverse@newSortedPair]
  ] &,
  {a, b},
  Min @ # > 1 &
];

DynamicModule[{a = 17, b = 10},
  EventHandler[
    Deploy @ Graphics[{PointSize @ 0.02,
        {Point @ #, Line @ #, PointSize @ 0.03, Red, Point @ First @ #} &@
          euclideanAlgorithmList[a, b] // Dynamic,
      Red, InfiniteLine[{0, 0}, {1, 1}]
    }, Frame -> True, GridLines -> Automatic,
    AspectRatio -> 1, PlotRange -> ConstantArray[{0, 20}, 2]
  ],
  {"MouseDragged" :> Set[{a, b}, Round /@ MousePosition["Graphics"]]}
  ]
]