Deanna has $44$ pieces of candy. What is the largest number of kids whom she can give an equal number of candies such that every kid gets at least $3$ pieces?
For $n$ kids to each get at least $3$ pieces of candy, there must be at least $3n$ pieces of candy, so we must have $3n\le 44$. Dividing both sides of this inequality by $3$, we have $n\le 14\frac23$. Since the number of kids must be an integer, the largest possible number of kids is $\boxed{14}$.