Which of the following is a prime number?

### Concept & Logic To identify a prime number, confirm that it has exactly two distinct factors: 1 and itself. Any even number greater than 2 is composite, and basic divisibility rules can quickly eliminate other composite numbers. ### Step-by-Step Solution * **Option (b) 20 and Option (d) 22:** Both are even numbers greater than 2. Thus, they are divisible by 2 and are composite. * **Option (c) 21:** The sum of the digits ($2 + 1 = 3$) is a multiple of 3. Thus, it is divisible by 3 ($21 = 3 \times 7$) and is composite. * **Option (a) 19:** 19 has no positive divisors other than 1 and itself. It is a prime number. ### Exam Strategy & Shortcut Use the process of elimination. Immediately cross out all even numbers (20, 22). Next, cross out numbers matching basic multiplication tables you know ($21 = 3 \times 7$). The remaining number (19) must be the answer. ### Common Pitfall Second-guessing if a smaller odd number like 19 has hidden factors. For numbers under 25, simply knowing your multiplication tables up to $5 \times 5$ is enough to be confident. ### Final Answer **Therefore, the correct answer is 19.**