📘CLASS 6 MATHS CHAPTER 3 – PLAYING WITH NUMBERS 📝 Competitive level

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🔹 Section A – Advanced MCQs (1 mark each)

  1. The number of factors of 36 is:
    a) 6 b) 7 c) 8 d) 9
  2. Which number has exactly 3 factors?
    a) 4 b) 6 c) 8 d) 10
  3. HCF of two consecutive numbers is always:
    a) 0 b) 1 c) 2 d) depends
  4. LCM of two co-prime numbers is:
    a) sum b) difference c) product d) 1
  5. Which number is divisible by 2, 3, and 5?
    a) 30 b) 45 c) 60 d) Both a & c
  6. The smallest number divisible by 8, 12, and 15 is:
    a) 60 b) 120 c) 240 d) 360
  7. Which is NOT co-prime?
    a) (8,15) b) (9,10) c) (14,21) d) (17,18)
  8. Number of prime numbers between 20 and 40:
    a) 4 b) 5 c) 6 d) 7
  9. HCF × LCM of two numbers =
    a) sum b) difference c) product d) square
  10. Which number leaves remainder 1 when divided by 2, 3, and 4?
    a) 11 b) 13 c) 25 d) 37

🔹 Section B – Integer & Logic Fill (2 marks each)

  1. The greatest 2-digit number divisible by 9 is ______
  2. The smallest 3-digit number divisible by 7 is ______
  3. If HCF = 5 and product = 500, LCM = ______
  4. A number divisible by 6 must be divisible by ______ and ______
  5. Number of factors of a prime number is ______

🔹 Section C – Short Answer (3 marks each)

  1. Find the number of factors of 72.
  2. Find the HCF of 36, 48, and 60.
  3. Find the LCM of 9, 12, and 15.
  4. Find prime factorization of 180.
  5. Find smallest number divisible by 4, 5, and 6.

🔹 Section D – Olympiad Case-Based (4 marks each)

📊 Case 1: School Parade Formation

  1. 84 boys and 126 girls are arranged in equal rows.
    a) Maximum number of rows
    b) Students per row
    c) Boys and girls per row

📊 Case 2: Digital Timer Problem

  1. Three alarms ring after every 6, 8, and 12 minutes.
    a) When will all ring together?
    b) How many times in 1 hour?

📊 Case 3: Packaging Factory

  1. Items packed in boxes of 18 and 24.
    a) Smallest equal number
    b) If 5 such batches made, total items?

📊 Case 4: Sports League

  1. Teams formed from 45 players so each team has equal players.
    Find all possible team sizes.

🔹 Section E – Long Answer (5 marks each)

  1. Find HCF and LCM of 48 and 180 using prime factorization.
  2. Verify: HCF × LCM = Product of numbers (use any two numbers)
  3. Find smallest number leaving remainder 2 when divided by 3, 4, and 5.
  4. Find the greatest number that divides 252 and 378 leaving remainder 0.

🔹 Section F – HIGH LEVEL HOTS (6 marks each)

  1. Find smallest number divisible by 2, 3, 4, 5, and 6 but not by 7.
  2. Find a number between 100 and 200 divisible by 9 and 12.
  3. Two numbers have HCF = 12 and LCM = 720
    Find the product and one possible pair.
  4. Find the least number which when divided by 8, 10, and 12 leaves remainder 3 in each case.

🔹 Section G – Assertion & Reason (3 marks each)

  1. Assertion: Every multiple of 6 is multiple of 3
    Reason: 6 = 2 × 3
  2. Assertion: Prime numbers have exactly 2 factors
    Reason: One factor is always itself
  3. Assertion: 1 is neither prime nor composite
    Reason: It has only one factor

🔹 Section H – MEGA CASE STUDY (10 marks)

📊 Case Study: Mega School Event

A school has:

  • 96 boys
  • 144 girls
  • 192 badges

They want to form equal groups such that:

  • Each group has same number of boys and girls
  • Each group gets equal badges
  1. Maximum number of groups
  2. Boys per group
  3. Girls per group
  4. Badges per group
  5. Identify concept used

✅ ANSWER KEY (Concise)

Section A:
1-d, 2-a, 3-b, 4-c, 5-d, 6-c, 7-c, 8-a, 9-c, 10-b

Section B:
11. 99
12. 105
13. 100
14. 2 and 3
15. 2

Section C:
16. 12 factors
17. 12
18. 180
19. 2×2×3×3×5
20. 60

Section D:
21. 42 rows; 2 boys, 3 girls
22. 24 min; 2 times
23. 72; 360
24. 1,3,5,9,15,45

Section E:
25. HCF=12, LCM=720
26. Verified
27. 62
28. 126

Section F:
29. 60
30. 108 or 180
31. Product=8640; pair (24,360)
32. 123

Section G:
33. True
34. True
35. True

Section H:
36. 48 groups
37. 2
38. 3
39. 4
40. HCF

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