📘CLASS 6 MATHS CHAPTER 3 – PLAYING WITH NUMBERS🌟 3.8 CO-PRIME NUMBERS (Worksheet)

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🌟 QUICK NOTES

🔹 What are Co-prime Numbers?

Two numbers are co-prime if their HCF = 1

👉 They have only one common factor → 1

🔹 Examples

  • (8, 15) → common factor = 1 ✔
  • (7, 9) → common factor = 1 ✔
  • (4, 9) → co-prime ✔

🔹 Not Co-prime

  • (6, 8) → common factors = 1, 2 → ❌
  • (12, 18) → common factors = 1, 2, 3, 6 → ❌

🔹 Important Points

  • Co-prime numbers may not be prime numbers
    👉 Example: 8 and 15 (both composite but co-prime)
  • Consecutive numbers are always co-prime
    👉 Example: 5 and 6

🔹 Key Idea

👉 If HCF = 1 → numbers are co-prime

📝 WORKSHEET – CO-PRIME NUMBERS

🔹 SECTION A (Very Short Answer)

  1. What is the HCF of co-prime numbers?
  2. Are 4 and 9 co-prime?
  3. Are 6 and 8 co-prime?
  4. Are 7 and 10 co-prime?
  5. Are 12 and 13 co-prime?
  6. Are 15 and 25 co-prime?
  7. Write any two co-prime numbers
  8. Write HCF of 8 and 15
  9. Are 9 and 16 co-prime?
  10. Are 14 and 21 co-prime?

🔹 SECTION B (Check Co-prime or Not)

  1. (8, 9)
  2. (10, 15)
  3. (14, 25)
  4. (18, 35)
  5. (21, 28)
  6. (16, 27)
  7. (12, 35)
  8. (20, 21)
  9. (9, 15)
  10. (17, 19)

👉 Write Co-prime / Not co-prime

🔹 SECTION C (Find HCF)

  1. HCF of 8 and 15
  2. HCF of 9 and 16
  3. HCF of 14 and 25
  4. HCF of 12 and 18
  5. HCF of 21 and 22

🔹 SECTION D (Concept Based)

  1. Are consecutive numbers always co-prime?
  2. Can two even numbers be co-prime?
  3. Can two prime numbers be co-prime?
  4. Can two composite numbers be co-prime?
  5. Which pair is co-prime: (6,7) or (6,9)?

🔥 SECTION E – CASE-BASED QUESTIONS

📖 Case Study 1: Number Cards

Cards show numbers: 4, 5, 6, 7

  1. Which pair is co-prime?
  2. Find two co-prime pairs

📖 Case Study 2: School Groups

Two groups have 8 and 15 students.

  1. Find HCF
  2. Are they co-prime?
  3. Why?

📖 Case Study 3: Puzzle

A pair has HCF = 1

  1. What are such numbers called?
  2. Give one example

📖 Case Study 4: Consecutive Numbers

  1. Are 20 and 21 co-prime?
  2. Give reason

📖 Case Study 5: Number Challenge

  1. Write two co-prime numbers between 10 and 20
  2. Write two co-prime odd numbers
  3. Write two co-prime even numbers (if possible)
  4. Write one co-prime pair where both are composite
  5. Write one co-prime pair where one is prime and one is composite
  6. Find HCF of 13 and 27
  7. Are 13 and 27 co-prime?
  8. Find HCF of 16 and 18
  9. Are they co-prime?
  10. Write two consecutive co-prime numbers
  11. Write smallest co-prime pair

✅ ANSWER KEY

SECTION A

  1. 1
  2. Yes
  3. No
  4. Yes
  5. Yes
  6. No
  7. Example: 8 and 15
  8. 1
  9. Yes
  10. No

SECTION B

  1. Co-prime
  2. Not
  3. Co-prime
  4. Co-prime
  5. Not
  6. Co-prime
  7. Co-prime
  8. Co-prime
  9. Not
  10. Co-prime

SECTION C

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

SECTION D

  1. Yes
  2. No (except 2 and 4? → still not)
  3. Yes
  4. Yes
  5. (6,7)

SECTION E

  1. (4,5), (5,6), (6,7), (5,7)
  2. Any two pairs above
  3. 1
  4. Yes
  5. Only common factor is 1
  6. Co-prime numbers
  7. Example: 7 and 8
  8. Yes
  9. Consecutive numbers
  10. Example: 11 and 12
  11. Example: 9 and 11
  12. Not possible (except trivial cases)
  13. Example: 8 and 15
  14. Example: 7 and 8
  15. 1
  16. Yes
  17. 2
  18. No
  19. Example: 15 and 16
  20. 1 and 2
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