Let P = QQQ be a 3-digit number. What is the HCF of P and 481?

A 3-digit number of the form QQQ (all three digits same) equals Q × 111 where Q is from 1 to 9. Note 111 = 3 × 37. Also 481 = 13 × 37. So both P and 481 share the common factor 37. The HCF of Q×111 and 481 = HCF(Q×3×37, 13×37) = 37 × HCF(3Q, 13). Since 13 is prime and 3Q for Q from 1-9 gives values 3,6,9,...,27, none of which are divisible by 13, HCF(3Q,13) = 1. Therefore HCF(P, 481) = 37 for all valid Q. The answer is (c) 37.