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

P = QQQ is a 3-digit number with all digits Q, so P = 111 × Q where Q is a single non-zero digit. 481 = 13 × 37. 111 = 3 × 37. So P = 3 × 37 × Q. The HCF of P and 481 will always include factor 37 (since 37 divides 111 and hence P, and 37 divides 481). The HCF could be 37 or 481, depending on whether 13 divides P. 13 divides 111 × Q only if 13 divides Q, but Q is a single digit (1-9), so 13 never divides Q. Therefore HCF(P, 481) = 37 for every valid Q.