 Assume that we wish to cover an "a"-by-"b" rectangle with square tiles exactly, where "a" is the larger of the two numbers.We first attempt to tile the rectangle using "b"-by-"b" square tiles; however, this leaves an "r"0-by-"b" residual rectangle untiled, where "r"0 0-by-"r"0 square tiles.This leaves a second residual rectangle "r"1-by-"r"0, which we attempt to tile using "r"1-by-"r"1 square tiles, and so on.