Prime identification by quick factoring Which of the following numbers is a prime number?

Introduction / Context: Determining primality quickly often involves testing divisibility by small primes. Here, each candidate can be checked by trying primes up to its square root and spotting easy factorizations.

Given Data / Assumptions:

• Candidates: 119, 187, 247.
• Test divisibility by 7, 11, 13, 17, 19, etc., up to √n.
• Composite if any nontrivial factor is found.

Concept / Approach: Use small-prime trials: check 7, 11, 13, 17, 19. Products of familiar pairs help (e.g., 7×17, 11×17, 13×19).

Step-by-Step Solution:119 = 7 × 17 ⇒ composite.187 = 11 × 17 ⇒ composite.247 = 13 × 19 ⇒ composite.Therefore, none of the listed numbers is prime.

Verification / Alternative check: Approximate square roots: √119 ≈ 10.9, √187 ≈ 13.7, √247 ≈ 15.7. All found factors are ≤ these, confirming valid checks.

Why Other Options Are Wrong:Each specific number factors nontrivially; selecting any would incorrectly assert primality.

Common Pitfalls: Stopping after testing 2, 3, 5 only; overlooking composite forms from recognizable products like 7×17 or 13×19.

Final Answer: None of these