Class 6 Mathematics – Chapter 5: Prime Time GANITA PRAKASH

Class 6 Mathematics – Chapter 5: Prime Time

🟢 Section A – Multiple Choice Questions (MCQs) 

1. Which of the following is a prime number?
   a) 21 b) 31 c) 51 d) 91 (Competency: Identify prime numbers)

2. The smallest prime number is:
   a) 0 b) 1 c) 2 d) 3 (Competency: Recall properties of primes)

3. Which number is neither prime nor composite?
   a) 0 b) 1 c) 2 d) 3 (Competency: Classify numbers as prime/composite)

4. The prime factorisation of 36 is:
   a) 2 × 3 × 6 b) 2² × 3² c) 6 × 6 d) 2 × 18 (Competency: Perform prime factorisation)

5. The HCF of 24 and 36 is:
   a) 6 b) 8 c) 12 d) 18 (Competency: Find common factors)

6. The LCM of 4 and 5 is:
   a) 10 b) 15 c) 20 d) 25 (Competency: Find common multiples)

7. Which of the following pairs are co-prime?
   a) 15 and 39 b) 20 and 55 c) 14 and 15 d) 12 and 26 (Competency: Identify co-prime numbers)

8. Prime factorisation of 84 is:
   a) 2 × 42 b) 2² × 3 × 7 c) 4 × 21 d) 2 × 2 × 21 (Competency: Factorise into primes)

9. The only even prime number is:
   a) 0 b) 2 c) 4 d) 6 (Competency: Recall special prime property)

10. Which of the following is a composite number?
    a) 17 b) 19 c) 20 d) 23 (Competency: Identify composite numbers)

11. The smallest common multiple of 3 and 5 is:
    a) 10 b) 15 c) 20 d) 30 (Competency: LCM understanding)

12. Which of the following numbers is divisible by 4?
    a) 152 b) 318 c) 624 d) 731 (Competency: Apply divisibility rules)

13. The prime factors of 56 are:
    a) 2, 7 b) 4, 14 c) 8, 7 d) 28, 2 (Competency: Prime factorisation)

14. Which is a twin prime pair?
    a) 7 and 9 b) 11 and 13 c) 15 and 17 d) 17 and 21  (Competency: Recognise twin primes)

15. The number 28 is called a perfect number because:
    a) It is prime b) Sum of its factors = twice the number c) It is even d) It is composite (Competency: Understand special numbers)

16. The product of first three prime numbers is:
    a) 30 b) 60 c) 12 d) 15 (Competency: Use prime multiplication)

17. Which of the following numbers is divisible by 5 but not by 10?
    a) 125 b) 140 c) 250 d) 400 (Competency: Apply divisibility rules)

18. If p and q are co-prime, then their HCF is:
    a) 0 b) 1 c) p × q d) p + q (Competency: Define co-primes) 

19. Which of the following numbers has exactly three distinct prime factors?
    a) 30 b) 45 c) 64 d) 49 (Competency: Identify prime factors)

20. The LCM of 8 and 12 is:
    a) 12 b) 16 c) 24 d) 48 (Competency: Find LCM)

🟠 Section B – Assertion and Reasoning 

Each question has two statements: Assertion (A) and Reason (R).
Choose the correct option:
a) Both A and R are true, and R is the correct explanation of A.
b) Both A and R are true, but R is not the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.

21. A: 2 is a prime number.
    R: A prime number has only two factors. (Competency: Define prime number)

22. A: 1 is neither prime nor composite.
    R: 1 has only one factor. (Competency: Classify 1 correctly)

23. A: The number 91 is prime.
    R: A prime number has exactly two factors. (Competency: Identify prime numbers)

24. A: 15 and 16 are co-prime numbers.
    R: Co-primes have no common factor other than 1. (Competency: Identify co-primes)

25. A: The HCF of 20 and 25 is 5.
    R: HCF is the largest common factor of two numbers. (Competency: Compute HCF)

26. A: All even numbers are composite.
    R: 2 is an even number. (Competency: Recognise exception)

27. A: 13 is a prime number.
    R: A prime number has more than 2 factors. (Competency: Prime vs composite)

28. A: The LCM of 9 and 12 is 36.
    R: LCM is the smallest number divisible by both. (Competency: Find LCM)

29. A: 7 is the only prime between 6 and 8.
    R: 7 has only two factors. (Competency: Identify prime correctly)

30. A: All prime numbers are odd.
    R: 2 is an even prime number. (Competency: Recall exceptions)

31. A: The prime factors of 60 are 2, 3 and 5.
    R: 60 = 2² × 3 × 5 (Competency: Perform prime factorisation)

32. A: Two consecutive numbers are always co-prime.
    R: Consecutive numbers differ by 1. (Competency: Co-prime property)

33. A: The number 28 is a perfect number.
    R: The sum of its factors is 56. (Competency: Define perfect numbers)

34. A: The number 51 is prime.
    R: Prime numbers cannot be divisible by 3. (Competency: Identify composites)

35. A: The product of two prime numbers is always composite.
    R: Composite numbers have more than two factors. (Competency: Properties of primes and composites)

36. A: 225 is divisible by 15.
    R: 225 ends with 25. (Competency: Apply divisibility)

37. A: HCF of 12 and 18 is 6.
    R: 6 divides both 12 and 18. (Competency: Find HCF)

38. A: The number 169 is prime.
    R: 169 = 13 × 13. (Competency: Identify squares)

39. A: The LCM of 4 and 6 is 12.
    R: 12 is divisible by both 4 and 6. (Competency: Find LCM)

40. A: Any two odd numbers are always co-prime.
    R: Odd numbers do not have common factors. (Competency: Check misconceptions)

🔵 Section C – True or False (10 Questions)

41. 2 is the only even prime number. (Competency: Recall prime property)

42. 1 is a prime number. (Competency: Classify 1)

43. All prime numbers are odd. (Competency: Exceptions in primes)

44. The number 57 is composite. (Competency: Identify composites)

45. The product of two primes can also be prime. (Competency: Prime properties)

46. Every composite number has more than two factors. (Competency: Define composite)

47. HCF of 9 and 12 is 3. (Competency: Find HCF)

48. LCM of 8 and 12 is 48. (Competency: Find LCM)

49. The number 100 is divisible by both 4 and 25. (Competency: Divisibility rules)

50. 121 is a prime number. (Competency: Identify squares)

🟣 Section D – Short Answer Type I 

51. Write the first five multiples of 7. (Competency: Generate multiples)

52. Find the factors of 24. (Competency: Identify factors)

53. Write prime factorisation of 45. (Competency: Prime factorisation)

54. State whether 15 and 16 are co-prime, with reason. (Competency: Co-prime check)

55. Find the HCF of 20 and 28. (Competency: Find HCF)

56. Find the LCM of 6 and 9. (Competency: Find LCM)

57. List prime numbers between 30 and 50. (Competency: Recall primes)

58. Write the smallest prime number greater than 100. (Competency: Recall prime)

59. Find the prime factors of 90. (Competency: Factorise into primes)

60. State whether 2 and 3 are co-prime. (Competency: Co-primes)

61. Find the smallest 3-digit prime number. (Competency: Recall primes)

62. Write two twin prime pairs below 20. (Competency: Twin primes)

63. Find the HCF of 48 and 60 using prime factorisation. (Competency: Apply prime factorisation)

64. Find the LCM of 15 and 20 using prime factorisation. (Competency: Apply prime factorisation)

65. Write all prime numbers less than 20. (Competency: Recall primes)

🟤 Section E – Short Answer Type II (3 Marks Each) 

66. Find the LCM and HCF of 24 and 36. (Competency: LCM & HCF)

67. Write prime factorisation of 108. (Competency: Prime factorisation)

68. Check whether 221 is prime or composite. (Competency: Test for primes)

69. Find the smallest number divisible by both 12 and 18. (Competency: Find LCM)

70. Write the first five multiples of 9 and 12, and find their common multiples. (Competency: Multiples & common multiples)

71. Show that 13 and 27 are co-prime. (Competency: Co-primes)

72. Find the prime factors of 72. (Competency: Prime factorisation)

73. Find the HCF of 32 and 48. (Competency: HCF)

74. State whether 2 consecutive numbers are always co-prime. Give an example. (Competency: Co-primes)

75. Express 84 as product of primes. (Competency: Prime factorisation)

🔴 Section F – Long Answer Type (5 Marks Each) [10 Questions]

76. Find the HCF and LCM of 96 and 404 by prime factorisation method. (Competency: HCF & LCM using prime factorisation)
    Write prime factorisation of 1000. (Competency: Prime factorisation)

77. Find the smallest number which is exactly divisible by 12, 18 and 24. (Competency: Find LCM)

78. Write all prime numbers between 1 and 100 using Sieve of Eratosthenes.

    
    
    (Competency: Prime identification)

79. Verify that 28 is a perfect number. (Competency: Properties of numbers)

80. Find the HCF of 65, 117 and 221. (Competency: HCF for 3 numbers)

81. If p = 2 × 3 × 5 and q = 2 × 5 × 7, find HCF(p, q) and LCM(p, q). (Competency: HCF & LCM)

82. Explain with example how to check divisibility of a number by 4. (Competency: Divisibility rules)

83. Find all twin primes between 1 and 100. (Competency: Recall twin primes)

84. Explain with example the difference between prime, composite and co-prime numbers. (Competency: Conceptual clarity)
    🟢 Section G – Case Based Questions (CBQ) 

Case Study 1 – Idli-Vada Game (NCERT Page 107)

A group of children play the Idli–Vada game sitting in a circle.The first child says “1”, the second says “2”, and so on.For numbers that are multiples of 3 (3, 6, 9, 12, …), the player says “idli” instead of the number.For numbers that are multiples of 5 (5, 10, 15, 20, …), the player says “vada” instead of the number.For numbers that are multiples of both 3 and 5 (like 15, 30, 45, …), the player says “idli-vada”.If any player makes a mistake, they are out of the game. The game continues until one person remains.Thus:Say idli → for multiples of 3.Say vada → for multiples of 5.Say idli-vada → for common multiples of 3 and 5.

Q1. Which of the following numbers will be replaced by “idli”?
a) 8 b) 9 c) 12 d) 14

Q2. Which of the following numbers should be replaced by “vada”?
a) 15 b) 20 c) 25 d) 27

Q3. The first number for which the player should say “idli-vada” is:
a) 30 b) 45 c) 15 d) 60

Q4. The numbers for which the player says “idli-vada” are:
a) Common multiples of 3 and 5 b) Multiples of 15 only
c) Prime numbers greater than 15 d) Multiples of 30 only

Q5. The LCM of 3 and 5 is:
a) 3 b) 5 c) 15 d) 30

86. What is the first number where “idli-vada” is said?
    a) 10 b) 12 c) 15 d) 30

87. How many times will “idli” be said between 1 and 30?
    a) 10 b) 12 c) 14 d) 9

88. Which numbers are called common multiples in this game?
    a) Multiples of 2 and 3 b) Multiples of 3 and 5 c) Multiples of 4 and 6 d) Multiples of 2 and 5

89. The 10th time “idli-vada” is said corresponds to which number?
    a) 120 b) 150 c) 90 d) 75

Case Study 2 – Jump Jackpot (NCERT Page 109)

Grumpy and Jumpy play a treasure game.Grumpy hides treasures on certain numbers.Jumpy selects a jump size and can only land on multiples of that jump size, starting from 0.If Jumpy lands on the treasure number(s), he wins them.

Situation 1: Single Treasure

Grumpy hides a treasure at 24.If Jumpy chooses a jump size of 4, he lands on 0 → 4 → 8 → 12 → 16 → 20 → 24 → 28 → … He wins the treasure.Other successful jump sizes are 1, 2, 3, 6, 8, 12, 24, since these are factors of 24.

Situation 2: Two Treasures

Grumpy hides two treasures at 14 and 36.If Jumpy chooses jump size 7, he lands on
0 → 7 → 14 → 21 → 28 → 35 → 42 → … He wins the treasure at 14,  but not at 36.The factors of 14 are: 1, 2, 7, 14.The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.👉 So, only 1 and 2 are common factors. Hence, jump sizes 1 and 2 allow Jumpy to win both treasures.

Q1. If Grumpy keeps a treasure at 24, which of the following jump sizes will NOT help Jumpy land on it?
a) 6 b) 8 c) 10 d) 12

Q2. The successful jump sizes for the treasure at 24 are:
a) Factors of 24 b) Multiples of 24 c) Prime numbers less than 24
d) Even numbers less than 24Q3. If treasures are at 14 and 36, which of these jump sizes will land Jumpy on both treasures?
a) 3 b) 2 c) 7 d) 9

Q4. The jump sizes that let Jumpy collect both treasures at 14 and 36 are:
a) All factors of 14 b) All factors of 36 c) Common factors of 14 and 36
d) Multiples of 14 and 36

Q5. The HCF (Highest Common Factor) of 14 and 36 is:
a) 14 b) 2 c) 7 d) 4

90. If the treasure is on 24, which jump size will not reach it?
    a) 2 b) 3 c) 5 d) 4

91. If treasures are on 14 and 36, which jump size will reach both?
    a) 7 b) 2 c) 14 d) 9

92. Common factors of 14 and 36 are:
    a) 1, 2 b) 2, 7 c) 2, 3 d) 1, 2, 3

93. Factors of 24 are:
    a) 1, 2, 3, 4, 6, 8, 12, 24 b) 2, 4, 8 c) 1, 3, 5, 7 d) 6, 12, 18

Case Study 3 – Co-prime Safekeeping (NCERT Page 115)
Treasures are safe if jump sizes cannot reach both numbers.
Let us go back to the treasure finding game. This time, treasures are kept in two numbers. Jumpy gets the treasures only if he is able to reach both the numbers with the same jump size. There is also a new rule — a jump size of 1 is not allowed. Where should Grumpy place the treasures so that Jumpy cannot reach both the treasures? Will placing the treasure on 12 and 26 work? No! If the jump size is chosen to be 2, then Jumpy will reach both 12 and 26. What about 4 and 9? Jumpy cannot reach both using any jump size other than 1. So, Grumpy knows that the pair 4 and 9 are safe..

94. Which of these is a co-prime pair?
    a) 15, 39 b) 4, 9 c) 12, 26 d) 20, 55

95. What is common in co-prime pairs?
    a) They have no common factor except 1 b) They are consecutive c) They are even d) They are divisible by 2

96. Co-prime of 18 is:
    a) 2 b) 3 c) 35 d) 9

97. Which pair is not co-prime?
    a) 4, 9 b) 15, 37 c) 81, 18 d) 30, 415

Case Study 4 – Divisibility Tests (NCERT Pages 123–125)
Students in a class are revising the rules of divisibility. These rules help in quickly checking whether a number is divisible by another, without performing the actual division.A number is divisible by 5 if it ends in 0 or 5. A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. A number is divisible by 4 if its last two digits form a number divisible by 4. A number is divisible by 10 if it ends in 0.

98. A number is divisible by 5 if it ends with:
    a) 0 b) 5 c) 0 or 5 d) 2

99. A number is divisible by 2 if it ends with:
    a) 1, 3, 5 b) 0, 2, 4, 6, 8 c) 0 only d) 2 only

100. Which of the following is divisible by 4?
     a) 232 b) 173 c) 125 d) 139

101. A number is divisible by 10 if:
     a) It ends with 0 b) It ends with 5 c) It ends with 2 d) It ends with 8

Case Study 5 – Fun with Numbers (NCERT Pages 126–127)
Students are comparing numbers for special properties. Some numbers are prime, some are perfect squares, and some are multiples of other numbers. A prime number has only two factors: 1 and itself. A square number is the product of a number with itself. Some numbers are special because of these unique properties.

102. Which is the only prime among 9, 16, 25, 43?
     a) 9 b) 16 c) 25 d) 43

103. 25 is special because:
     a) It is a square b) It is multiple of 5 c) It is even d) It is prime

104. 16 is special because:
     a) It is a multiple of 3 b) It is even and multiple of 4 c) It is odd d) It is prime

105. A 9 is special because:

a) It is a single-digit number b) It is a multiple of 3 c) It is odd d) Both (a) and (b)