The other night, my son and I worked out all the primes less than 100. It started when I was showing him how to look at division problems (or fractions) like 12 * 6 / 4. Not only how to factor but how multiplication and division are commutative together and between factoring and ordering of operations, problems that look difficult are actually not. In any event, we were factoring a couple numbers and it led to us just finding all of the primes less than 100. By this time they know pretty well the easy divisibility rules, 2, 5 and 10, 11 (10 is actually redundant for this purpose). By the time we got to 50, he was pretty sure of himself when I would call out the numbers in succession and he would answer "No" for all the obvious composites (those that ended in 0,2,4,5,6, or 8) and would pause as he tried to recall a multiplication fact for the others. I showed him the rule for divisibility by 3. The only number that got by us was "91" which is 7*13. Of course it would be a ! number involving 7 and 13. We didn't have a rule for 7 and 13 was outside of his multiplication facts.
Some lessons seem just the right lesson at just the right time. This was one of them. It noticeably increased his awareness of and ability in factoring.