This is a seemingly simple problem - hopefully someone can help.
Problem: we have two integers. We want (1) all the common factors, and
(2) all the possible products of these factors. We know how to get (1),
but can't figure out a general way to get (2).

 

Example: 40 and 80 have these factors: c(1,2,2,2,5) and c(1,2,2,2,2,5).
We can use match() to get the common factors c(1,2,2,2,5). What we want
to be able to get from this is the list of all the possible products,
which should be the concatenation of the original list, the products of
all the pairs, of all the triplets, and so forth:
c(1,2,2,2,5,4,8,10,20,40). 

 

The application is this: we have an area that is, say, 40 x 80 units. We
want to find all the possible grids (of square integer-valued units)
that can be placed over that area that cover it completely. The list at
the end of the preceding paragraph is the right answer - the question is
how to get it from our list of common factors, other than by brute
force.

 

Thanks for any advice.

 

Gordon

 

--

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

 


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