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The above can be coded to remove the extra modulo; however, it either requires a variable declaration for each level of recursion or an extra recursive call (the base case would be if y = 0, meaning if x mod y = 0 we would make one more call wehereas here we simply return). All three implementations are valid, only depending on what is most efficient for the language and processor (in C++, modulo is an inline operation so the above is generally fastest, but other languages require a less-efficient Mod(x,y) function call).
Below is the same algorithm using an iterative approach:
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