Classification — primes vs composite: identify the single number that does NOT belong with the primes.

Introduction / Context:
Number classification frequently contrasts prime numbers with a lone composite. You need to find the only number that has nontrivial divisors besides 1 and itself.

Given Data / Assumptions:

• 19, 29, 23 are well-known primes.
• 27 is 3 * 3 * 3 (i.e., 3^3), thus composite.

Concept / Approach:
Apply primality checks: for two-digit candidates under 30, test divisibility by small primes (2, 3, 5).

Step-by-Step Solution:
1) 19 → not divisible by 2, 3, 5 → prime.2) 29 → not divisible by 2, 3, 5 → prime.3) 23 → not divisible by 2, 3, 5 → prime.4) 27 → divisible by 3 (27 = 3 * 9) → composite.5) Therefore 27 is the unique non-prime.

Verification / Alternative check:
Digit-sum test for divisibility by 3: 2+7=9 → divisible by 3, confirming compositeness for 27.

Why Other Options Are Wrong:
19, 29, and 23 pass basic divisibility tests and are primes.

Common Pitfalls:
Mistaking 29 for composite; recall that 25 and 27 are composites, but 29 is prime.

Final Answer:
27