Let P = QQQ be a 3-digit number. What is the HCF of P and 481 ?
- (a) 1
- (b) 13
- (c) 37 ✓ UPSC's answer
- (d) 481
Why the answer is (c)
• Let P = QQQ, which can be expressed as 100Q + 10Q + Q = 111Q.
• Factorize 111 to find its prime components: 111 = 3 × 37.
• Therefore, P = 3 × 37 × Q.
• Factorize 481 to find its prime components: 481 = 13 × 37.
• The common factor between P (which contains 37) and 481 (which contains 37) is 37.
• Since 37 is the highest common factor, the HCF of P and 481 is 37.
Why the other options are wrong
- (a) 1
- 1 is incorrect because both numbers share the common factor 37, so the HCF is greater than 1.
- (b) 13
- 13 is incorrect because 13 is a factor of 481 but not necessarily a factor of P (111Q), as 111 is not divisible by 13.
- (d) 481
- 481 is incorrect because 481 is not a factor of P (111Q) for any single digit Q, as 111 is not a multiple of 481.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.