In the UK, `factor' is synonymous with `divisor' and the term `prime factor' is used to refer to the things that appear in the unique factorisation into irreducibles. Also, I haven't seen `gcf' anywhere, but children learn `hcf' (`highest common factor') -- which is even worse since it's defined in terms of the total order on Z, rather than merely the multiplicative structure. And nowhere (before undergraduate level) is unique factorisation ever justified. Sincerely, Adam P. Goucher
Sent: Monday, May 25, 2015 at 1:12 PM From: "Bill Gosper" <billgosper@gmail.com> To: math-fun@mailman.xmission.com Subject: [math-fun] gcF??
Perhaps because they're taught factorization rather than Euclid's algorithm, gradeschoolers are now being forced to say gcf ("greatest common factor") instead of gcd. Or maybe just to make it sound easier. So I asked a kid: 12 contains how many factors of 3? And how many factors of 2? And how many factors of 1? "Tell your teacher 1 can't be a factor of anything. 2 and 3 have no greatest common factor." "I'll get in trouble."
A lot of stuff we're taught is oversimplified. We have to unlearn it and relearn it later. But this is ridiculous. Is there some way we funsters can gang up against this idiocy? --rwg They're also taught that improper fractions are not in lowest terms. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun