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

Answer: (c) 37

Every number of the form QQQ equals Q × 111 = Q × 3 × 37, and 481 = 13 × 37. They always share the factor 37, and 13 can never divide 3Q for a single digit Q, so the HCF is 37.

1. QQQ = Q × 111 = Q × 3 × 37.
2. 481 = 13 × 37.
3. HCF = 37 × HCF(3Q, 13). For a single digit Q, 3Q is at most 27 and is never 13 or 26, so HCF(3Q, 13) = 1.
4. So the HCF of P and 481 is 37, whatever the digit Q.
5. Check: HCF(222, 481) = 37, since 222 = 6 × 37 and 481 = 13 × 37.

Remember · Repeated-digit numbers: aaa = a × 3 × 37. Knowing 111 = 3 × 37 settles such items at sight.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error