Use Euclid's algorithm. If the remainder from division of the larger by the smaller is zero, then the smaller is the GCF; otherwise, the remainder replaces the larger, and the algorithm repeats.
(4/9)/(3/7) = 1 remainder 1/63*
(3/7)/(1/63) = 27 remainder 0
The GCF is 1/63.
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* The quotient is 28/27 = 1 +1/27 = 1 +(1/27)(3/7)/(3/7) = 1 +(1/63)/(3/7) or 1 with a remainder of 1/63.