If all the \(N\) students of a class are classified into groups of either \(n,\) or \(n+1,\) or \(n+2\) students, every time \(3\) students are left out and cannot be included in any of those groups formed. What is the value of \(N?\)

1. \(N\) is between \(7\) and \(70.\)
2. \(n\) is the smallest number with exactly \(3\) distinct factors.

Answer: A

Source: e-GMAT