Choose the odd number: In 143, 257, 195, and 15, three are composite, while one is prime. Identify the prime number.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Prime vs composite classification: factor quickly to isolate the prime. Given Data / Assumptions: 143 = 11 * 13. 195 = 3 * 5 * 13. 15 = 3 * 5. 257 = ? Concept / Approach:Test divisibility for 257 by small primes up to sqrt(257) ≈ 16 (i.e., 2, 3, 5, 7, 11, 13). Step-by-Step Solution: 257 mod 2 ≠ 0; mod 3 → 2+5+7=14 → not divisible; mod 5 → not 0 or 5; mod 7, 11, 13 → not divisible.Thus 257 has no small factors → prime.143, 195, 15 are composite by explicit factorization. Verification / Alternative check:Nearby products show no 257 = p * q with small primes; hence prime. Why Other Options Are Wrong:Each factors non-trivially (11*13, 3*5*13, 3*5). Common Pitfalls:Assuming a number near a square (16^2=256) must be composite; 257 is prime. Final Answer:257 is the odd number (prime).

Choose the odd number: In 143, 257, 195, and 15, three are composite, while one is prime. Identify the prime number.

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