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#Python 3, 31
Saved 3 bytes thanks to Sp3000.
g=lambda a,b:b and g(b,a%b)or a
Or for a 21 (saved 5 thanks to Sp3000) byte solution,
from math import*;gcd
#Python 3, 4031
defg=lambda g(a,b): b whileand g(b:a,b=b,a%b return)or a
#Python 3, 40
def g(a,b): while b:a,b=b,a%b return a
