Which of the following numbers is not a prime number?

Introduction / Context:
This question tests the basic concept of prime numbers. A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Any number with more than two positive divisors is called a composite number. Here we must identify which option is not prime, that is, which number has additional divisors besides 1 and itself.

Given Data / Assumptions:

• The options given are 5, 11, 21, 37, and 41.
• We assume the standard definition of prime numbers.
• We check each candidate by trying to factor it into smaller positive integers.
• We only need to find the one that is clearly composite.

Concept / Approach:
To test whether a number n is prime, we try to divide it by all prime numbers less than or equal to sqrt(n). If none of these primes divides n exactly, then n is prime. For relatively small numbers like those given, we can check divisibility by small primes such as 2, 3, 5, and 7. A composite number will factor into a product of smaller integers greater than 1.

Step-by-Step Solution:
Step 1: Check 5. It is not divisible by 2, 3, or any other smaller prime except 1 and 5, so 5 is prime.Step 2: Check 11. It is not divisible by 2, 3, or 5. The only positive divisors are 1 and 11, so 11 is prime.Step 3: Check 21. Test divisibility by 2: 21 is odd, so not divisible by 2. Test divisibility by 3: 2 + 1 = 3, and 3 divides 21, so 21 = 3 * 7.Step 4: Since 21 has divisors 1, 3, 7, and 21, it is not prime; it is composite.Step 5: Check 37. It is not divisible by 2, 3, or 5. The only positive divisors are 1 and 37, so 37 is prime.Step 6: Check 41 similarly. 41 is not divisible by 2, 3, or 5. It has only 1 and 41 as divisors and is therefore prime.Step 7: The only non prime (composite) number among the options is 21.

Verification / Alternative check:
You can confirm 21 is composite using divisibility rules. The sum of its digits is 2 + 1 = 3, which is divisible by 3, so 21 is divisible by 3. Dividing 21 by 3 gives 7, so 21 = 3 * 7. Since it clearly has factors other than 1 and itself, it cannot be prime. For the other numbers, quick divisibility checks by small primes show no exact divisors apart from 1 and the number itself.

Why Other Options Are Wrong:
Option 5: 5 has only divisors 1 and 5, so it is prime and does not satisfy the condition of being non prime.Option 11: 11 is a standard example of a prime number greater than 10.Option 37: 37 is not divisible by any prime less than or equal to 6, making it a prime number.Option 41: 41 is also a prime number; it has no divisors other than 1 and 41.

Common Pitfalls:
Students sometimes confuse prime and composite numbers or assume that any odd number is prime, which is not true. For example, 21 is odd but composite. Another mistake is not checking divisibility by all relevant small primes, such as forgetting to test divisibility by 3 or 7. Always recall that a prime number greater than 2 is odd, but not every odd number is prime. Factorisation or divisibility tests are essential to be sure.

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