Techniques for Factoring Numbers in Your Head

I’ve been factoring times while I walk my son to sleep, and it’s become kind of a game: can I factor the current time faster than he can fall asleep? After a few big matches, he’d developed quite a win streak, and I needed to up my game. I kept getting bogged down in the double digits. I needed a way to check a number’s divisibility faster than doing the mental long division.