Which of the following numbers is a prime number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 167
A number is prime if no prime up to its square root divides it. Since \(13^2=169\), for 167 it is enough to test 2, 3, 5, 7 and 11.
167 is odd, so 2 does not divide it
Digit sum \(1+6+7=14\), so 3 does not divide it
It does not end in 0 or 5, so 5 does not divide it
\(167=7\times23+6\) and \(167=11\times15+2\), so neither 7 nor 11 divides it
So 167 is a prime number.
Why the other options are incorrect
Option (2) 350 — Incorrect. It ends in 0, so it is divisible by 10.
Option (3) 437 — Incorrect. \(437=\) \(19\times23\).
Option (4) 213 — Incorrect. Its digit sum is 6, so it is divisible by 3: \(213=\) \(3\times71\).