Editing Euclidean algorithm (section)

=== Visualization ===
The Euclidean algorithm can be visualized in terms of the tiling analogy given above for the greatest common divisor.<ref name="Kimberling_1983">{{cite journal | last = Kimberling|first= C.|author-link=Clark Kimberling | year = 1983 | title = A Visual Euclidean Algorithm | journal = Mathematics Teacher | volume = 76 | pages = 108–109}}</ref> Assume that we wish to cover an {{math|''a''×''b''}} rectangle with square tiles exactly, where {{math|''a''}} is the larger of the two numbers. We first attempt to tile the rectangle using {{math|''b''×''b''}} square tiles; however, this leaves an {{math|''r''<sub>0</sub>×''b''}} residual rectangle untiled, where {{math|''r''<sub>0</sub> < ''b''}}. We then attempt to tile the residual rectangle with {{math|''r''<sub>0</sub>×''r''<sub>0</sub>}} square tiles. This leaves a second residual rectangle {{math|''r''<sub>1</sub>×''r''<sub>0</sub>}}, which we attempt to tile using {{math|''r''<sub>1</sub>×''r''<sub>1</sub>}} square tiles, and so on. The sequence ends when there is no residual rectangle, i.e., when the square tiles cover the previous residual rectangle exactly. The length of the sides of the smallest square tile is the GCD of the dimensions of the original rectangle. For example, the smallest square tile in the adjacent figure is {{math|21×21}} (shown in red), and {{math|21}} is the GCD of {{math|1071}} and {{math|462}}, the dimensions of the original rectangle (shown in green).