Does the integer k have a factor p such that 1 < p < k ?

Question

Does the integer k have a factor p such that 1 < p < k ?

Answer 1

The key to answering this question (and doing so quickly) is to understand what information the question stem is giving us. In this case, if k has a factor, p, such that 1< p < k, then what the question is really asking us is: "is k a composite number?". The only way for k not to have a factor p that is between 1 and k is if k is prime.