Which of the following numbers is a prime number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 283
A number is prime if no prime up to its square root divides it. Each option is tested; for 283 the remainders are never 0.
\(17^{2}=289\) is more than 283, so it is enough to test the primes 2, 3, 5, 7, 11, 13
283 is odd and its digit sum 13 is not a multiple of 3, and it does not end in 0 or 5
\(283=7\times40+3\), \(283=11\times25+8\), \(283=13\times21+10\)
So 283 is a prime number.
Why the other options are incorrect
Option (1) 287 — Incorrect. \(287=7\times41\), so it is not prime.
Option (2) 299 — Incorrect. \(299=13\times23\), so it is not prime.
Option (3) 289 — Incorrect. \(289=17\times17\), so it is not prime.