Insomniac fun

When I can't sleep, I play with numbers. Sometimes I pick a random number - say 351 and then count backwards by sevens. Other times, I hunt for primes. Lately, I've been trying to figure out how to apply a divison rule to multiples of seven. For example, you can always tell if a number is divisible by 9 if you add all the digits together and they equal 9. Take 45, 4+5 = 9, so 45 is divisible by 9.

I couldn't discern any pattern by adding digits together, but it usually got me to sleep eventually.

I should have just Googled it. I was never going to find the division rule of 7 the way I was going. I happened to stumble across it when I was looking for something else.

Here it is:

To find out if a number is divisible by seven, take the last digit, double it,
and subtract it from the rest of the number. Example: If you had 203, you would
double the last digit to get six, and subtract that from 20 to get 14. If you
get an answer divisible by 7 (including zero), then the original number is
divisible by seven. If you don't know the new number's divisibility, you can
apply the rule again.

You can find that rule and a whole lot more at the math forum.