Math and You
posted in Hurray for Geekdom, fathers |One of the things I’m happy about from my childhood is the math. Yeah, this is where I remind dad that he wouldn’t let me have a calculator until I didn’t need one. Math and I get along pretty well. It’s kind of odd that reluctance to do math contributed to my dropping out of the Chemistry path in college, though. I enjoyed science too- especially Chem but I got tired of doing the “where could the electron be” equations and finally gave up.
Anyway, the DQ was doing her homework last night and asked me if some large ungainly number like 23001 could be divisible by three. I told her that 2+3+1 was 6 and 6 was a multiple of three, so yes. I think I picked that rule up in Junior High. We were doing some sort of factoring exercise and the teacher showed us that rule. So we could do any number was divisible by 2, 5, 10, and now 3, 6, 9 too ( if it’s divisible by 2 and also 3 then it’s divisible by 6, if the numbers add up to a multiple of 9 then it’s also divisible by nine ). I could never remember the fairly complicated rule for sevens, though. “Sevens are hard” I told DQ last night.
Ms B was surprised to learn that rule of threes. She caught on quick though 
because she’s a smart cookie. She agreed that sevens are hard.
So in my daily news reading, I was surprised to come across this article: “Is 91 Prime?” . One of those strange coincidences of the world.
Here’s their answer to the sevens conundrum:
Is 8638 divisible by 7?
863 - 2*8 = 847 (subtract twice the last digit)
84 - 2*7 = 70 (subtract twice the last digit)
70 = 7 * 10, which is divisible by 7 -- therefore 8638 is divisible by 7
That seems like too much work to me. It’s actually faster in this case for me to look at “7 goes into 8638… goes into 8 remainder 1, goes into 16 remainder 2, goes into 23 remainder 2, goes into 28 even, so yes. Sort of a division only worrying about the remainder.
Anyway, that article actually explains why the threes rule above works. It has to do with the decimal system. I almost understand it. One of the comments was also very interesting about square roots: the difference of two square roots is not prime. So 91 is not prime ( sorry to spoil the ending ) because 1) seven goes into 9 remainder 2 then seven goes into 21 remainder 0 and 2) (10×10)-(3×3)=91.
Easy, huh? What about 133? Are there two squares that differ by 133?
