Consider the numbers (i) 263, (ii) 221, and (iii) 483. Which of these are prime and composite numbers?

Correct Answer: (i) is prime, while (ii) and (iii) are composite.

Subject: 2025

• (i) and (ii) are composite, while (iii) is prime.
• (i) is prime, while (ii) and (iii) are composite.
• All are composite.
• All are prime.

Explanation: <b>Key Fact</b><br>• 263 is a prime number (not divisible by any prime up to √263 ≈ 16: 2, 3, 5, 7, 11, 13).<br>• 221 = 13 × 17 (Composite).<br>• 483 = 3 × 161 = 3 × 7 × 23 (Composite).<br><br><b>Additional Info</b><br>Topic: Number Systems.<br><br><b>Why the other options are wrong</b><br>Option A: 221 is composite, but 483 is also composite.<br>Option B: Correct.<br>Option C: Incorrect because 263 is prime.<br>Option D: Incorrect because 221 and 483 are composite.<br><br><b>Exam Trick</b><br>Test divisibility rules: 4+8+3 = 15 (divisible by 3, so composite). 221 = 13 × 17 is a standard test case.<br><br><b>Final Answer</b><br>Option B — (i) is prime, while (ii) and (iii) are composite.