When you see a fraction, you see a numerator and a denominator. To find the common factor, see whichever number among these is least: The numerator, the denominator or the difference between numerator and denominator.
Take your time. You don’t need to sit down and learn all of the multiplication facts at one time. In fact, this would be the worst way to learn. Choose a table and focus solely on that one. Take as much time as you need to master each one before moving onto the next one. Spend about 15-20 minutes each day studying flashcards or playing math games to master each multiplication fact. There are many multiplication math games with different themes that can be found online. For instance, if you really like dinosaurs, find one that uses dinosaurs to make learning more fun.