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
4. D. 481

Answer: C

Explanation

To find the HCF (Highest Common Factor) of P and 481, we first need to express both numbers in their prime factorized form.

1. **Analyze P = QQQ**: A 3-digit number QQQ can be written as Q × 100 + Q × 10 + Q × 1 = Q × (100 + 10 + 1) = Q × 111. Since P is a 3-digit number, Q must be a digit from 1 to 9. Now, factorize 111: 111 = 3 × 37. So, P = Q × 3 × 37.

2. **Factorize 481**: We test for prime factors. 481 is not divisible by 2, 3, 5, 7, 11. Trying 13: 481 ÷ 13 = 37. So, 481 = 13 × 37.

3. **Find HCF**: The HCF of P (Q × 3 × 37) and 481 (13 × 37) is the product of their common prime factors. The only common prime factor is 37. Since Q is a single digit (1-9), it cannot be 13. Therefore, the HCF is 37. This question tests basic number theory, specifically factorization and finding the Highest Common Factor, which is a fundamental concept in quantitative aptitude for CSAT.