When my son* was small we played the Factor Game. Enter some random big number into the calculator, start dividing and see where it leads you.
Oh, and then there was the Rhode Island game, with the aid of an atlas that gave the area of each state. How many Rhode Islands can fit into it? (For those who like to know: the answers range from three for Delaware to around 500 for Alaska.)
Phone numbers are always easier to remember when they mean something. Like my longago optometrist whose number ended in 1066 -- hard to forget that one -- or the professor who helpfully pointed out that his phone number was the date of the battle of Tours. (This was not quite as helpful as he thought. 0732 maybe?)
* The one who grew up to be a math major. Gee, I wonder how that happened.