Classification – Odd one out (unique prime among composites) Exactly one of the following integers is prime while the others are composite. Identify the prime number and mark it as the odd one out.

Introduction / Context:Prime-versus-composite classification is common. The fastest route is to eliminate obvious composites by small-prime checks (2, 3, 5, 7, 11, 13, …) and then test the surviving candidate up to its square root.

Given Data / Assumptions:

• Candidates: 488, 776, 667, 929
• We look for the single prime.

Concept / Approach:First discard even numbers (composite if > 2): 488 and 776 are even. Next check 667: it equals 23 * 29 (composite). The remaining number 929 must be tested up to sqrt(929) ≈ 30.5 against primes 3, 5, 7, 11, 13, 17, 19, 23, 29. None divides 929 evenly, making it prime.

Step-by-Step Solution:488 → even → composite.776 → even → composite.667 → 23 * 29 → composite.929 → not divisible by 3, 5, 7, 11, 13, 17, 19, 23, 29 → prime.

Verification / Alternative check:Trial division up to 29 confirms no exact divisor for 929; therefore it is prime. All others have explicit composite factorizations or are even > 2.

Why Other Options Are Wrong:

• 488: Composite (even).
• 776: Composite (even).
• 667: Composite (23 * 29).
• None of these: There is a unique prime (929).

Common Pitfalls:Stopping at parity checks only. While parity helps, you must also test odd candidates against small primes to avoid mislabeling.

Final Answer:929