A common technique is to remember the following time and date :
Real Value: 6.02 x 10^23 atoms/mole.
Trick: 6:02 a.m. on October 23
October - signifies the value 10
a.m. - signifies the unit atoms/mole
It's fairly easy to memorize the value since we use it frequently, but you tend to forget it suddenly while doing calculations. With this small trick in mind you're never going to have trouble in recalling the value.