Out of the following numbers, which one is not a prime number and therefore is a composite number?

Introduction:
Prime numbers are fundamental in number theory and aptitude tests often include quick checks of whether a number is prime or composite. This question asks you to identify which of the given options is not prime, meaning it has factors other than 1 and itself.

Given Data / Assumptions:

• We are given the integers 5, 11, 21, 37, and 19.
• A prime number has exactly two distinct positive divisors: 1 and the number itself.
• A composite number has additional divisors besides 1 and itself.

Concept / Approach:
To test primality of relatively small numbers, we try to divide each by small prime numbers such as 2, 3, 5, and 7. If a number is divisible by any of these (without remainder) and is greater than that small prime, it is composite. If it is not divisible by any prime less than or equal to its square root, then it is prime.

Step-by-Step Solution:
Step 1: Check 5. It is divisible only by 1 and 5. So 5 is prime. Step 2: Check 11. It is divisible only by 1 and 11. So 11 is prime. Step 3: Check 21. Try division by 3: 21 / 3 = 7 exactly, so 21 has factors 1, 3, 7, and 21. Step 4: Since 21 has divisors other than 1 and itself, it is composite, not prime. Step 5: Check 37 briefly. 37 is not divisible by 2, 3, 5, or any other prime up to sqrt(37), so it is prime. Step 6: Check 19 briefly. 19 is also not divisible by any smaller prime except 1 and itself, so it is prime.

Verification / Alternative check:
You can also list factor pairs. For 21 we have (1, 21) and (3, 7). The presence of the pair (3, 7) immediately confirms that 21 is composite. None of the other numbers produce such nontrivial factor pairs.

Why Other Options Are Wrong:

• 5, 11, 19, and 37 each have only two positive divisors: 1 and the number itself. Therefore, these are all prime numbers and cannot be the correct answer.

Common Pitfalls:
Some test takers quickly guess based on familiarity and might overlook that 21 is a multiple of 7 and 3. Others sometimes confuse 19 or 37 as composite due to their larger size. Always do a quick divisibility check using small primes to avoid such mistakes.

Final Answer:
The number that is not a prime number is 21.