Any number where the individual digits add up to a number divisible by ‘3’ is divisible by 3.

51 = 5+1 = 6, which is divisible by three.

Try it, you’ll see it always works.

There are tricks like that for a lot of numbers. For 7, chop off the last digit, double it and add it to what’s left. Repeat as required. If the result is divisible by 7 then the original number was. eg: 356 -> 35+12=47 not db7. 357 =>35+14 both db7 so we don’t even need to do the add.

Clever.