In the following question, four whole numbers are given. Three of them are prime numbers and one is composite. Select the composite number (odd one out).

Introduction / Context:
This question tests basic number theory concepts that often appear in aptitude and competitive exams. Specifically, it checks whether the learner can distinguish prime numbers from composite numbers. Recognising prime numbers is an essential skill for many reasoning and quantitative topics, including divisibility, factors, and advanced arithmetic problems.

Given Data / Assumptions:
- The options are five positive integers: 13, 17, 21, 23, and 19.
- We use the standard definition of a prime number as a number greater than 1 with exactly two distinct positive factors, 1 and the number itself.
- A composite number has more than two positive factors.
- Exactly one number among the options is composite and different from the others.

Concept / Approach:
The approach is to test each number for primality by checking if it has any divisor other than 1 and itself. Small numbers can be checked quickly by testing divisibility with small primes such as 2, 3, 5, and 7. If a number is divisible by one of these and is larger than that prime, then it is composite. For this question, it is enough to check divisibility by 3 and other small primes, because the numbers are not very large.

Step-by-Step Solution:
Step 1: Check 13. It is not divisible by 2, 3, or 5. Therefore, 13 is a prime number.Step 2: Check 17. It is not divisible by 2, 3, or 5. Therefore, 17 is a prime number.Step 3: Check 23. It is not divisible by 2, 3, or 5. Therefore, 23 is a prime number.Step 4: Check 19. It is not divisible by 2, 3, or 5. Therefore, 19 is also a prime number.Step 5: Now check 21. It is divisible by 3 because 2 + 1 = 3, which is divisible by 3. We can also write 21 = 3 * 7, so it clearly has factors other than 1 and itself.Step 6: Since 21 is divisible by 3 and 7, it is composite, while all the other options are prime numbers. Therefore, 21 is the odd one out.

Verification / Alternative Check:
We can verify quickly by listing the factors of each number. The factors of 13 are 1 and 13 only. For 17, the factors are 1 and 17. For 23, the factors are 1 and 23. For 19, the factors are 1 and 19. In contrast, the factors of 21 are 1, 3, 7, and 21, which shows that it is composite. Since exactly one number has more than two factors, our classification is correct and the reasoning is consistent.

Why Other Options Are Wrong:
13 is not the odd one out because it is a prime number like 17, 19, and 23. 17 is also a prime and therefore similar to 13, 19, and 23, so it cannot be the unique different option. 23 is prime as well and does not stand out when compared with 13, 17, and 19. 19 is another prime number and therefore fits into the same group as the other primes. Only 21 is composite and therefore qualifies as the odd one out.

Common Pitfalls:
Students sometimes confuse 21 with a prime number because it is not an obvious multiple like 20 or 24. Another common mistake is to test divisibility only by 2 and 5, forgetting to check for 3 and 7. In exams, always test divisibility by the smallest primes first. If a number is not divisible by any of them, only then treat it as prime. This habit will reduce careless mistakes in similar odd one out questions.

Final Answer:
21