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

⭐ Composite Numbers – Detailed Description

  • A Composite Number is a natural number greater than 1 that has more than two factors.
  • This means composite numbers can be divided by 1, itself, AND at least one more number.

Set Representation

  • Composite numbers ⊂ Natural Numbers but exclude 1 and prime numbers.

Examples

  • 4 → factors: 1, 2, 4
  • 6 → factors: 1, 2, 3, 6

Key Properties of Composite Numbers

  • A composite number has more than two divisors.
  • 1 is neither prime nor composite.
  • 2 is the only even prime, but every even number > 2 is composite.
  • The smallest composite number is 4.
  • All composite numbers can be expressed as a product of primes (Prime Factorization).
  • There are infinitely many composite numbers.
  • Composite numbers include:
    • Even composite numbers (4, 6, 8, 10…)

    • Odd composite numbers (9, 15, 21, 25…)

5 Examples of Composite Numbers (with Explanation)

  1. 4: Factors: 1, 2, 4 → more than 2 factors.
  2. 6: Factors: 1, 2, 3, 6 → composite.
  3. 8: Factors: 1, 2, 4, 8 → composite.
  4. 9: Factors: 1, 3, 9 → composite (odd composite number).
  5. 15: Factors: 1, 3, 5, 15 → composite.

MCQ's For Exam

Q.1. Which is the smallest composite number?

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

4) 4

📝Explanation: 4 has factors 1, 2, 4 → 3 factors → composite.

Q.2. Which of the following is a composite number?

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

3) 9

📝 Description: 9 = 3 × 3 → composite.

Q.3. Composite numbers have:

  1. Only two factors
  2. More than two factors
  3. Only one factor
  4. No factors

2) More than two factors

📝 Description: Composite = more than two factors.

Q.4. Which number is NOT composite?

  1. 4
  2. 6
  3. 8
  4. 13

4) 13

📝 Description: 13 is prime.(Have only 2 factors 1 & Itself)

Q.5. Is 1 a composite number?

  1. Yes
  2. No
  3. Sometimes
  4. Depends

2) No

📝 Description: 1 has only one factor.

Q.6. Which of these is composite?

  1. 17
  2. 19
  3. 21
  4. 23

3) 21

📝 Description: 21 = 3 × 7.

Q.7. Which even number is composite?

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

2) 4

📝 Description: All even numbers > 2 are composite.

Q.8. The number 10 is composite because:

  1. It is odd
  2. Factors are 1, 2, 5, 10
  3. It is prime
  4. It has only 2 factors

2) Factors are 1, 2, 5, 10

📝 Description: More than two factors → composite.

Q.9. How many composite numbers are between 1 and 10?

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

4) 4

📝 Description: Composite numbers: 1 → 4, 6, 8, 9 → 10 = Total 4

Q.10. Which of the following numbers is composite?

  1. 25
  2. 29
  3. 31
  4. 37

1) 25

📝 Description: 25 = 5 × 5.

Q.11. 45 is a composite number because:

  1. 45 is even
  2. 45 has factors 1, 3, 5, 9, 15, 45
  3. 45 is odd
  4. 45 is prime

2) 45 has factors 1, 3, 5, 9, 15, 45

📝 Description: Many factors → composite.

Q.12. Which number is composite?

  1. 49
  2. 53
  3. 59
  4. 61

1) 49

📝 Description: 49 = 7 × 7.

Q.13. Which pair BOTH contains composite numbers?

  1. (9, 11)
  2. (15, 21)
  3. (5, 25)
  4. (7, 49)

2) 15 & 21

📝 Description: 15 & 21 are composite.

Q.14. How many composite numbers are there between 20 and 30?

  1. 5
  2. 6
  3. 7
  4. 8

3) 7

📝 Description: 20 → 21, 22, 24, 25, 26, 27, 28 → 30 = Total 7

Q.15. 27 is composite because:

  1. 27 is even
  2. 27 has 3 factors
  3. 27 = 3 × 9
  4. All of these

3) 27 = 3 × 9

📝 Description: Factorization → composite(More than 2 factors)

Q.16. The prime factorization of 72 is:

  1. 2³ × 3²
  2. 2² × 3³
  3. 2⁴ × 3
  4. 2 × 3²

1) 2³ × 3²

📝 Description: 72 = 2 × 2 × 2 × 3 × 3.

Q.17. Which number is GUARANTEED to be composite?

  1. n × (n + 1)
  2. n
  3. n – 1
  4. n + 2

1) n × (n + 1)

📝 Description: Product of two consecutive numbers → never prime.

Q.18. The number 121 is composite because:

  1. It ends in 1
  2. 121 = 11 × 11
  3. It is odd
  4. It is greater than 50

2) 121 = 11 × 11

📝 Description: Non-prime factorization.

Q.19. Which of these numbers is composite?

  1. 91
  2. 97
  3. 101
  4. 103

1) 91

📝 Description: 91 = 7 × 13.

Q.20. If a number has exactly 4 factors, it is:

  1. Always prime
  2. Always composite
  3. Always odd
  4. Cannot be determined

2) Always composite

📝 Description: Prime numbers have only two factors; more → composite.

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