i have a goal to play through the challenge mode on Difficult setting without letting the Multiples of 7/13/17/19 be run-killers -- it's pretty hard to do the mental math on the fly but i'm going to try practicing the following shortcuts on three digit numbers...

multiple of 7: 2 times the last digit, minus the rest, is a multiple of 7

multiple of 13: 4 times the last digit, plus the rest, is a multiple of 13

multiple of 17: 5 times the last digit, minus the rest, is a multiple of 17

multiple of 19: 2 times the last digit, plus the rest, is a multiple of 19

let's see how it goes?!