Which of the following numbers is a prime number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 239
A number is prime if no prime up to its square root divides it. Each option is tested; for 239 the remainders are never 0.
\(16^{2}=256\) is more than 239, so it is enough to test the primes 2, 3, 5, 7, 11, 13
239 is odd and its digit sum 14 is not a multiple of 3, and it does not end in 0 or 5
\(239=7\times34+1\), \(239=11\times21+8\), \(239=13\times18+5\)
So 239 is a prime number.
Why the other options are incorrect
Option (1) 253 — Incorrect. \(253=11\times23\), so it is not prime.
Option (3) 259 — Incorrect. \(259=7\times37\), so it is not prime.
Option (4) 247 — Incorrect. \(247=13\times19\), so it is not prime.