"L'esprit de l'escalier" strikes again....
An even simpler statement of your original problem:
Find the factors that A and B have in common.
If A and B are fairly small (< 1e7, say), a very direct approach is:
which( ! (A %% 1:min(A,B)) & !(B %% 1:min(A,B)) )
Is this "brute force"? Well, I suppose, but it is simple and direct
and fast enough for A=B=1e7 (5 sec). It doesn't involve factorization
into prime factors, GCDs, or combinations.
If your goal is concision and not clarity or speed, you can do even better:
which( !(A %% 1:B & B %% 1:A) )
which is still practical (though it gives a warning).
How big do your A and B get, and how many different A's and B's do you
need to run this calculation for?
-s
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