Student: So how can I factor numbers more easily?
Me: You'll have to know the multiplication tables really well.
Student: Ok. But how can I know what the factors are without dividing every time?
Me: Knowing the multiplication table backwards and forwards will help you to eventually memorize the factors of the most commonly used numbers.
Student: That's so much work! There has to be a better way.
Me: Not until you can recite the multiplication tables without hesitation.
There are short cuts to factorization, but I didn't want to tell this student what they were without forcing them to do it the long way first. Really now. Short cuts will just get you more lost than before, if you don't know how to read a map to begin with.