UPSC Prelims 2025·CSAT·Quantitative Aptitude·Number System

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

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Last updated 23 May 2026, 3:31 pm IST
  1. A1
  2. B13
  3. C37Correct
  4. D481

Explanation

To solve this, we first express P based on its digits. Since P is QQQ, it can be written as 100Q + 10Q + Q, which equals 111 multiplied by Q. Next, we factorize the two numbers: 1. P = 111 multiplied by Q. The number 111 can be broken down into 3 multiplied by 37. So, P = 3 multiplied by 37 multiplied by Q. 2. The number 481 can be factorized into 13 multiplied by 37. To find the Highest Common Factor (HCF), we look for the common factors between P and 481. The number 37 is a factor of both 111 (and thus P) and 481. While Q could theoretically be 13, in a 3-digit number QQQ, Q must be a single digit from 1 to 9. Therefore, Q cannot be 13. This means 13 is not a common factor. The only certain common factor between P and 481 is 37. Thus, the HCF is 37.
Quantitative Aptitude: Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
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