All the products of common factors

Thanks for all the suggestions!

The tricky part isn't finding the common factors -- we knew how to do
that, though not in so concise a fashion as some of these suggestions.
It was finding all their products without what I (as a recovered Fortran
programmer) would call "truly brute force." Several of these suggestions
solve the problem nicely!

Gordon

P.S. The numbers involved will never be very large -- these are
dimensions of areas in which trees were sampled, in meters. They'll
always be on the order of 50-100m or so on a side.
--
Dr. Gordon A. Fox       Voice: (813)974-7352       Fax: (813)974-3263
Dept. of Integrative Biology ((for US mail:)SCA 110) ((for FedEx
etc:)NES 107)
Univ. of South Florida                 4202 E. Fowler Ave.
Tampa, FL 33620, USA                   http://foxlab.cas.usf.edu

"All the fun of sitting still, being quiet, writing down numbers. Yes,
science has it all." -- Principal Skinner


-----Original Message-----
From: macrakis at gmail.com [mailto:macrakis at gmail.com] On Behalf Of
Stavros Macrakis
Sent: Wednesday, February 25, 2009 2:02 AM
To: Fox, Gordon; r-help at r-project.org
Subject: Re: [R] All the products of common factors

Argh!  The second (concise) version should have |, not & !!!

          -s

"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