GATE General Aptitude and CS Solutions Practice Test 2026 - Free GATE Practice Questions and Study Guide

Primality means a natural number greater than 1 that has exactly two positive divisors: 1 and itself. To test a number, check divisibility by small integers up to the square root of the number. For 23, it isn’t divisible by 2 (it’s odd) and it isn’t divisible by 3 (the sum of digits is 5, not a multiple of 3). Since √23 is about 4.8, testing 2 and 3 is enough, and it passes. That means 23 has no divisors other than 1 and 23, so it is prime. The other numbers can be factored as 15 = 3×5, 21 = 3×7, and 25 = 5×5, so they are not prime.