Which of the following is not a prime number?

### Concept & Logic A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. A composite number has at least one positive divisor other than 1 or itself. ### Step-by-Step Solution * **Check Option (a):** $21$ The sum of the digits is $2 + 1 = 3$. According to the divisibility rule of 3, 21 is divisible by 3. $$21 = 3 \times 7$$ Since 21 has factors other than 1 and itself, it is not a prime number. * **Check Remaining Options:** $23$, $29$, and $43$ are only divisible by 1 and themselves. They are all prime numbers. ### Exam Strategy & Shortcut When asked to find the non-prime (composite) number among small values, always check for basic divisibility rules first: particularly for 2 (even numbers), 3 (sum of digits), and 5 (ends in 0 or 5). 21 immediately triggers the rule for 3. ### Common Pitfall Failing to check basic divisibility rules and instead trying to mentally divide by larger, random numbers, which wastes time. Always start with the smallest primes. ### Final Answer **Therefore, the correct answer is 21.**