Let $P = QQQ$ be a 3-digit number. What is the HCF of P and 481?
Let $P = QQQ$ be a 3-digit number. What is the HCF of P and 481?
1
13
37
481
Solution
A 3-digit number with all identical digits is $QQQ = Q \times 111 = Q \times 3 \times 37$. So every such number is a multiple of 37. Now $481 = 13 \times 37$. The common factor of $P = Q\times3\times37$ and $481 = 13\times37$ is 37 (the digit Q is 1-9, none of which is a multiple of 13). Hence HCF = 37.