Which of the following numbers is a prime number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 331
A number is prime if no prime up to its square root divides it. Each option is tested; for 331 the remainders are never 0.
\(19^{2}=361\) is more than 331, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17
331 is odd and its digit sum 7 is not a multiple of 3, and it does not end in 0 or 5
\(331=7\times47+2\), \(331=11\times30+1\), \(331=13\times25+6\), \(331=17\times19+8\)
So 331 is a prime number.
Why the other options are incorrect
Option (1) 323 — Incorrect. \(323=17\times19\), so it is not prime.
Option (3) 341 — Incorrect. \(341=11\times31\), so it is not prime.
Option (4) 343 — Incorrect. \(343=7\times49\), so it is not prime.