P.S. But here's something that may help you remember:

Imagine an illiterate medieval крестьянин (peasant) trying to count how many apples he has by referring to the number of legs on a cow.

He can count 2, 3, or 4 apples using the legs of just one cow (genitive singular). But to count 5 or more apples, he needs the legs of a second cow (genitive plural)!