Prime Numbers
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Prime Numbers – Definition, Properties, Examples & 20 Solved MCQs for Competitive Exams

⭐ Prime Numbers – Detailed Description

  • A Prime Number is a natural number greater than 1 that has exactly two distinct positive factors1 and the number itself
  • This means a prime number cannot be divided evenly by any other number.

List of First Few Prime Numbers

  • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …

Key Properties of Prime Numbers

  • A prime number has only two factors → 1 and itself.
  • 1 is NOT a prime number (only one factor).
  • 2 is the only even prime number — all other even numbers are composite.
  • Every natural number greater than 1 is either prime or composite.
  • Prime numbers are the building blocks of all natural numbers (Prime Factorization).
  • There are infinitely many primes — proven by Euclid.
  • Prime numbers help in cryptography, coding theory, and mathematics.

5 Examples of Prime Numbers (With Explanation)

  1. 2: Only even prime, divisible by 1 and 2 only.
  2. 3: Factors: 1, 3 → prime.
  3. 7: Divisible only by 1 and 7.
  4. 11: No divisor other than 1 and 11.
  5. 19: Cannot be divided evenly by any number except 1 and 19.

MCQ's For Exam

Q.1. Which is the smallest prime number?

  1. 0
  2. 1
  3. 2
  4. 3

3) 2

📝Explanation: 2 is the smallest and only even prime number.

Q.2. How many factors does a prime number have?

  1. One
  2. Two
  3. Three
  4. Many

2) Two

📝 Description: Only 1 and itself.

Q.3. Which number is NOT a prime number?

  1. 7
  2. 11
  3. 9
  4. 13

3) 9

📝 Description: 9 = 3 × 3 → composite.

Q.4. Is 1 a prime number?

  1. Yes
  2. No
  3. Sometimes
  4. Cannot say

2) No

📝 Description: 1 has only ONE factor, not two.

Q.5. Which of these is a prime number?

  1. 15
  2. 21
  3. 17
  4. 25

3) 17

📝 Description: Only divisible by 1 and 17.

Q.6. Which one is the only even prime number?

  1. 4
  2. 6
  3. 2
  4. 8

3) 2

📝 Description: All even numbers > 2 are divisible by 2.

Q.7. How many prime numbers are there between 1 and 10?

  1. 3
  2. 4
  3. 5
  4. 6

2) 4

📝 Description: Prime numbers: 1 → 2, 3, 5, 7 →  10 = Total 4

Q.8. Which of the following is a prime number?

  1. 27
  2. 31
  3. 39
  4. 49

2) 31

📝 Description: Other options have multiple factors.

Q.9. Is 29 a prime number?

  1. Yes
  2. No
  3. Depends
  4. Only sometimes

1) Yes

📝 Description: 29 has no divisors except 1 and 29.

Q.10. Which number is composite?

  1. 2
  2. 5
  3. 9
  4. 13

3) 9

📝 Description: Composite → more than 2 factors.

Q.11. Which number is prime?

  1. 51
  2. 53
  3. 57
  4. 63

2) 53

📝 Description: 51 = 3×17, 57 = 3×19, 63 = 7×9.

Q.12. Which is a pair of prime numbers?

  1. (9, 11)
  2. (13, 17)
  3. (21, 23)
  4. (15, 19)

2) 13 & 17

📝 Description: Both 13 and 17 are prime.

Q.13. How many prime numbers are between 20 and 30?

  1. 1
  2. 2
  3. 3
  4. 4

2) 2

📝 Description: Prime numbers: 20 → 23, 29 →  30 = Total 2

Q.14. Which of the following is NOT a prime number?

  1. 41
  2. 47
  3. 49
  4. 43

3) 49

📝 Description: 49 = 7 × 7. So 1, 7, 49

Q.15. The next prime after 37 is:

  1. 38
  2. 39
  3. 41
  4. 43

3) 41

📝 Description: 38, 39, 40 are composite.

Q.16. Which of these is a prime triplet?

  1. 3, 5, 7
  2. 5, 7, 9
  3. 7, 9, 11
  4. 9, 11, 13

1) 3, 5 & 7

📝 Description: All three are prime numbers.

Q.17. Which number below is definitely NOT prime?

  1. 61
  2. 71
  3. 81
  4. 97

3) 81

📝 Description: 81 = 9 × 9. So, 1, 9, 81

Q.18. If a number ends in 5, it is prime only when:

  1. It is equal to 5
  2. It is odd
  3. It is divisible by 3
  4. It has 3 factors

1) It is equal to 5

📝 Description: Any number ending in 5 is divisible by 5 → composite, except 5 itself.

Q.19. Which number is PRIME among the following?

  1. 91
  2. 93
  3. 97
  4. 99

3) 97

📝 Description: 

  • 91 = 7 × 13
  • 93 = 3 × 31
  • 99 = 9 × 11
    97 is prime.

Q.20. A prime number greater than 3 is always of the form:

  1. 5n
  2. 6n
  3. 6n ± 1
  4. 6n ± 3

3) 6n ± 1

📝 Description: All primes ≥ 5 fit 6n – 1 or 6n + 1 pattern.

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