Correct me if I'm wrong, but divisibility is only a partial order (and thus 
gcds are only unique) modulo associates. Everything but 0 is a unit in 
Z/7Z, an integral domain, so any of 1, 2, 3, 4, 5, or 6 would be an 
acceptable value for the gcd of 5 and 7(=0), no? Or is the "common parent" 
something other than Z/7Z? I do see

sage: gcd(Integers(7)(5), 7)
5
sage: gcd(Integers(7)(5), 7).parent() is ZZ
True

which makes no sense.

-Keshav

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