Practice Questions
Concept Explanation
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. 1 is neither prime nor composite.
Prime Numbers up to 50
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Prime Factorisation
Every composite number can be written uniquely as a product of primes. Example: 360 = 2³ × 3² × 5.
Tests for Primality
To check if n is prime, test division by primes up to √n. If none divide exactly, n is prime.
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Q1 EasyWhich one of the following is not a prime number?Explanation91 is divisible by 7. So, it is not a prime number.
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Q2 EasyWhich of the following is a prime number?ExplanationClearly, 97 is a prime number. 33, 81 and 93 are composite.
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Q3 EasyThe sum of first five prime numbers is:ExplanationRequired sum = (2 + 3 + 5 + 7 + 11) = 28. Note: 1 is not a prime number.
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Q4 EasyThe smallest 3 digit prime number is:Explanation100 is not prime. 101 is not divisible by any prime below √101, so 101 is the smallest 3-digit prime.
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Q5 EasyThe smallest prime number is:Explanation2 is the smallest prime number and the only even prime.
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Q6 EasyWhat is the prime factorisation of 84?Explanation84 = 2 × 2 × 3 × 7 = 2² × 3 × 7.
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Q7 EasyWhich is the largest prime number less than 30?Explanation29 is prime; 27 and 28 are composite.
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Q8 EasyWhich of the following numbers is composite?Explanation45 = 9 × 5, so it is composite.
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Q9 MediumHow many prime numbers are less than 50?ExplanationPrimes less than 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Their number is 15.
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Q10 MediumHow many prime numbers are there between 20 and 40?ExplanationPrimes between 20 and 40: 23, 29, 31, 37 → 4 primes.
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Q11 MediumHow many distinct prime factors does 210 have?Explanation210 = 2 × 3 × 5 × 7 → 4 distinct prime factors.
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Q12 MediumWhich pair consists of twin primes?ExplanationTwin primes differ by 2 and both must be prime. 17 and 19 qualify. 21, 25 and 27 are composite.
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Q13 MediumWhat is the product of the first three prime numbers?ExplanationFirst three primes: 2, 3, 5. Product = 30.
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Q14 HardHow many distinct prime numbers divide 100 exactly?Explanation100 = 2² × 5². Distinct prime divisors: 2 and 5 → 2.
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DS1 Easy
In a cryptography warm-up exercise, you need the smallest prime factor of the integer N. What is the smallest prime factor of N?
Statement IN = 91.
Statement IIN is composite.
Explanation91 = 7 × 13, so the smallest prime factor is 7. Statement II alone does not identify N. -
DS2 Medium
Before encrypting a message, a candidate must confirm whether N is prime. Is the positive integer N a prime number?
Statement IN is odd.
Statement IIN is greater than 2.
Explanation9 is odd and greater than 2 but composite. Many odd numbers satisfy both statements without being prime.
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DS3 Medium
During prime factorisation practice, how many distinct prime factors does the integer N have?
Statement IN = 2³ × 7.
Statement IIN is divisible by 14.
ExplanationFrom the prime form, distinct prime factors are 2 and 7 → 2. Statement II alone (e.g. N = 14 or 28) does not fix the count. -
DS4 Hard
Twin primes appear in a reasoning set. Is N a twin prime (i.e., both N and N + 2 are prime)?
Statement IN = 17.
Statement IIN + 2 is prime.
ExplanationN = 17 gives N + 2 = 19, also prime — N is a twin prime. Neither statement alone fixes both N and N + 2.