I've played around with numbers enough to have found some interesting things you can do with them. Some of the rules below I figured out for myself, others I gleaned from the web or newsgroups.

The idea I'll deal with here is a relatively useless set of tests, since pocket calculators are so easy to use (and I'm not sure of an immediate use anyway, even if it were hard to come up with an answer in another way).

That idea is whether or not any given number is evenly divisible by some number (i.e. leaves no remainder when divided by that number).

In elementary school you probably had to do some of this. Every number is evenly divisible by one. Every even number is evenly divisible by two. But one thing that always interested me was how one found whether or not something was divisible by three: sum the digits, and if the sum was divisible by three, then the total number was also divisible by three. I never really got a decent explanation as to why this was true back in grade school, and I hadn't given the problem any further thought until I saw a comment on one of the math newsgroups dealing with a test for whether or not a number was evenly divisible by seven. The poster's ideas were rather interesting, but I found the explanation to be a bit more confusing than it needed to be. Since I found the ideas to be sufficiently interesting, I thought I'd present my version for many different numbers.

I've decided to use JavaScript to make the interface a bit friendlier. If you have trouble with it, e-mail me ([email protected]) and I'll try to fix the problem.