Hatim and Arithmetic

Arithmetic is Hatim's favorite subject, but what spoils it for him is that Riya is in his class, and she is better than him at it. Prime numbers are of mystical importance in Arithmetics, and Lucky Numbers even more so. Lucky Numbers are those positive integers that have at least three distinct prime factors; 30 and 42 are the first two. Hatim's teacher has given them a positive integer n, and has