Which of the following numbers is a prime number?

The correct answer is Option (3) → 211

A number is prime if no prime up to its square root divides it. Each option is tested; for 211 the remainders are never 0.

• \(15^{2}=225\) is more than 211, so it is enough to test the primes 2, 3, 5, 7, 11, 13

• 211 is odd and its digit sum 4 is not a multiple of 3, and it does not end in 0 or 5

• \(211=7\times30+1\), \(211=11\times19+2\), \(211=13\times16+3\)

So 211 is a prime number.

Why the other options are incorrect

• Option (1) 209 — Incorrect. \(209=11\times19\), so it is not prime.

• Option (2) 217 — Incorrect. \(217=7\times31\), so it is not prime.

• Option (4) 221 — Incorrect. \(221=13\times17\), so it is not prime.