The smallest three-digit prime number is

### Concept & Logic To find the smallest three-digit prime number, start with the first three-digit number ($100$) and check subsequent numbers for primality. A number is prime if its only divisors are 1 and itself. ### Step-by-Step Solution * **Check 100:** 100 is an even number, thus divisible by 2. It is composite. * **Check 101:** We only need to test for divisibility by prime numbers up to the approximate square root of 101. $$\sqrt{101} \approx 10$$ The primes to test are 2, 3, 5, and 7. - Not divisible by 2 (it is odd). - Not divisible by 3 (sum of digits $1 + 0 + 1 = 2$). - Not divisible by 5 (does not end in 0 or 5). - Not divisible by 7 ($101 \div 7$ leaves a remainder of 3). Since no prime up to its square root divides it evenly, 101 is a prime number. ### Exam Strategy & Shortcut There is no complex calculation needed here. Memorizing the first few prime numbers immediately following 100 (101, 103, 107, 109) is highly recommended for quantitative aptitude exams to save precious seconds. 101 is the smallest. ### Common Pitfall Overthinking or confusing 101 with a number that looks prime but isn't. Some students guess "None of these" assuming a trap, but basic sequential testing proves 101 is the answer. ### Final Answer **Therefore, the correct answer is 101.**