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 three-digit 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 2007-09-16 19:30:17