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 Easy
Which of the following is a prime number?
Explanation59 has no divisors other than 1 and 59. 51=3×17, 57=3×19, 63=7×9. -
Q2 Medium
How many prime numbers are there between 20 and 40?
ExplanationPrimes: 23, 29, 31, 37 → 4 primes. -
Q3 Easy
What is the smallest prime number?
Explanation2 is the smallest and the only even prime. -
Q4 Easy
The prime factorisation of 84 is:
Explanation84 = 2×2×3×7 = 2² × 3 × 7. -
Q5 Easy
Which is the largest prime less than 30?
Explanation29 is prime; 27 and 28 are composite. -
Q6 Medium
How many prime factors does 210 have (distinct)?
Explanation210 = 2 × 3 × 5 × 7 → 4 distinct prime factors. -
Q7 Easy
If p is prime and p > 2, then p is:
ExplanationEvery prime greater than 2 is odd (2 is the only even prime).
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Q8 Medium
Which pair are twin primes?
ExplanationTwin primes differ by 2 and both must be prime. 17 and 19 qualify. 21, 25, 27 are composite. -
Q9 Medium
The sum of prime factors of 30 (with repetition) is:
Explanation30 = 2 × 3 × 5. Sum = 2 + 3 + 5 = 10. -
Q10 Easy
Which number is composite?
Explanation45 = 9 × 5, so it is composite. -
Q11 Hard
How many primes divide 100 exactly?
Explanation100 = 2² × 5². Distinct prime divisors: 2 and 5 → 2. -
Q12 Easy
If n = 2³ × 3², how many prime factors (distinct) does n have?
ExplanationDistinct primes are 2 and 3 → 2. -
Q13 Easy
Which is the only even prime?
Explanation2 is the only even prime number. -
Q14 Medium
The product of first three primes is:
ExplanationFirst three primes: 2, 3, 5. Product = 30.
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DS1 Medium
Is the positive integer N prime?
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. -
DS2 Easy
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.
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DS3 Hard
Is N a twin 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. -
DS4 Medium
How many distinct prime factors does N have?
Statement IN = 2³ × 7.
Statement IIN is divisible by 14.
ExplanationFrom prime form, distinct prime factors are 2 and 7 → 2. Statement II alone (e.g. N = 14 or 28) does not fix the count.