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For questions on divisors and multiples, mainly but not exclusively of integers, and related and derived notions such as sums of divisors, perfect numbers and so on.

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When does $2$ arise when using the Euclidean algorithm to compute greatest common divisors?

When using the standard Euclidean algorithm to compute the greatest common divisor of a pair of relatively prime positive integers, the integer $2$ sometimes arises and sometimes does not. For example …