You can decide whether a number is divisible by 3 by forming its cross sum,
that is the sum of all its decimal digits: It is divisible by three exactly if its cross sum is. Similarly, a threedigit number is
divisible by seven if (and only if) the sum of twice its most significant
digit plus three times its middle digit plus its least significant digit is
divisible by seven.
Can you find a similar scheme for checking divisibility by 33 and 37, for numbers with an arbitrary number of digits?
If i put it into my calculator and it doesn't come up with one of those decimal point thingys, then it is divisible by 33 or 37.

Posted by jduval
on 20070916 19:30:17 