UPSC Prelims 2025 CSAT Paper II · Q77 of 78 Basic Numeracy medium

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

  1. (a) 1
  2. (b) 13
  3. (c) 37 ✓ UPSC's answer
  4. (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.

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