🌟 QUICK NOTES (HCF)

🔹 What is HCF?

The Highest Common Factor (HCF) is the greatest number that divides two or more numbers exactly.

👉 Also called Greatest Common Divisor (GCD)

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🔹 Method 1: Listing Factors

✅ Example: Find HCF of 12 and 18

Factors of 12 → 1, 2, 3, 4, 6, 12
Factors of 18 → 1, 2, 3, 6, 9, 18

👉 Common factors → 1, 2, 3, 6
👉 HCF = 6

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🔹 Method 2: Prime Factorisation

✅ Example: Find HCF of 24 and 36

24 = 2³ × 3
36 = 2² × 3²

👉 Common primes with smallest powers
👉 HCF = 2² × 3 = 12

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🔹 Important Points

• HCF is always ≤ smallest number
• If HCF = 1 → numbers are co-prime
• Used in equal grouping / distribution problems

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📝 WORKSHEET – HCF (EXERCISE 3.4)

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🔹 SECTION A (Very Short Answer)

1. Find HCF of 8 and 12
2. Find HCF of 10 and 15
3. Find HCF of 6 and 9
4. Find HCF of 14 and 21
5. Find HCF of 16 and 24
6. What is the HCF of two equal numbers?
7. What is the HCF of two co-prime numbers?
8. Find HCF of 7 and 13
9. Find HCF of 18 and 27
10. Find HCF of 20 and 30

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🔹 SECTION B (Using Factors Method)

11. Find HCF of 12 and 18
12. Find HCF of 15 and 25
13. Find HCF of 16 and 20
14. Find HCF of 21 and 28
15. Find HCF of 24 and 30
16. Find HCF of 9 and 15
17. Find HCF of 18 and 24
18. Find HCF of 14 and 35
19. Find HCF of 25 and 30
20. Find HCF of 32 and 48

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🔹 SECTION C (Prime Factorisation Method)

21. Find HCF of 36 and 48
22. Find HCF of 60 and 90
23. Find HCF of 72 and 108
24. Find HCF of 45 and 75
25. Find HCF of 84 and 126

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🔥 SECTION D – CASE-BASED QUESTIONS

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📖 Case Study 1: Chocolate Distribution

Riya has 12 chocolates and Meena has 18 chocolates.

26. What is the maximum number of equal groups they can make?
27. How many chocolates will each group have?

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📖 Case Study 2: Ribbon Cutting

A ribbon of 24 cm and another of 36 cm are to be cut into equal pieces.

28. What is the greatest length of each piece?
29. How many pieces from each ribbon?

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📖 Case Study 3: School Arrangement

There are 20 boys and 30 girls.

30. What is the maximum number of equal groups?
31. How many students in each group?

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📖 Case Study 4: Number Puzzle

32. Two numbers have HCF = 1
    👉 What are such numbers called?
33. Give one example

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📖 Case Study 5: Factory Problem

A factory packs 36 and 48 items into equal boxes.

34. What is the maximum number of boxes?
35. How many items per box?

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🔥 SECTION E – THINKING QUESTIONS

36. Can HCF be greater than the numbers?
37. Find HCF of 1 and any number
38. Which has greater HCF: (8,12) or (9,15)?
39. Find two numbers whose HCF is 5
40. Find two co-prime numbers

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🔹 SECTION F (Mixed Practice)

41. Find HCF of 27 and 36
42. Find HCF of 16 and 40
43. Find HCF of 18, 24 and 30
44. Find HCF of 12, 18 and 24
45. Find HCF of 20, 25 and 30
46. Find HCF of 14, 28 and 42
47. Find HCF of 9, 27 and 81
48. Find HCF of 8, 16 and 32
49. Find HCF of 15, 45 and 60
50. Find HCF of 21, 42 and 63

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✅ ANSWER KEY

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SECTION A

1. 4
2. 5
3. 3
4. 7
5. 8
6. Same number
7. 1
8. 1
9. 9
10. 10

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SECTION B

11. 6
12. 5
13. 4
14. 7
15. 6
16. 3
17. 6
18. 7
19. 5
20. 16

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SECTION C

21. 12
22. 30
23. 36
24. 15
25. 42

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SECTION D

26. 6
27. 2 and 3 (groups distribution concept)
28. 12 cm
29. 2 and 3 pieces
30. 10
31. 5
32. Co-prime numbers
33. Example: 8 and 15
34. 12
35. 3 and 4

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SECTION E

36. No
37. 1
38. Both equal (HCF = 4 and 3 → compare: 4 > 3 so first)
39. Example: 10 and 15
40. Example: 7 and 9

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SECTION F

41. 9
42. 8
43. 6
44. 6
45. 5
46. 14
47. 9
48. 8
49. 15
50. 21