๐ QUICK NOTES
๐น What are Co-prime Numbers?
Two numbers are co-prime if their HCF = 1
๐ They have only one common factor โ 1
๐น Examples
- (8, 15) โ common factor = 1 โ
- (7, 9) โ common factor = 1 โ
- (4, 9) โ co-prime โ
๐น Not Co-prime
- (6, 8) โ common factors = 1, 2 โ โ
- (12, 18) โ common factors = 1, 2, 3, 6 โ โ
๐น Important Points
- Co-prime numbers may not be prime numbers
๐ Example: 8 and 15 (both composite but co-prime) - Consecutive numbers are always co-prime
๐ Example: 5 and 6
๐น Key Idea
๐ If HCF = 1 โ numbers are co-prime
๐ WORKSHEET โ CO-PRIME NUMBERS
๐น SECTION A (Very Short Answer)
- What is the HCF of co-prime numbers?
- Are 4 and 9 co-prime?
- Are 6 and 8 co-prime?
- Are 7 and 10 co-prime?
- Are 12 and 13 co-prime?
- Are 15 and 25 co-prime?
- Write any two co-prime numbers
- Write HCF of 8 and 15
- Are 9 and 16 co-prime?
- Are 14 and 21 co-prime?
๐น SECTION B (Check Co-prime or Not)
- (8, 9)
- (10, 15)
- (14, 25)
- (18, 35)
- (21, 28)
- (16, 27)
- (12, 35)
- (20, 21)
- (9, 15)
- (17, 19)
๐ Write Co-prime / Not co-prime
๐น SECTION C (Find HCF)
- HCF of 8 and 15
- HCF of 9 and 16
- HCF of 14 and 25
- HCF of 12 and 18
- HCF of 21 and 22
๐น SECTION D (Concept Based)
- Are consecutive numbers always co-prime?
- Can two even numbers be co-prime?
- Can two prime numbers be co-prime?
- Can two composite numbers be co-prime?
- Which pair is co-prime: (6,7) or (6,9)?
๐ฅ SECTION E โ CASE-BASED QUESTIONS
๐ Case Study 1: Number Cards
Cards show numbers: 4, 5, 6, 7
- Which pair is co-prime?
- Find two co-prime pairs
๐ Case Study 2: School Groups
Two groups have 8 and 15 students.
- Find HCF
- Are they co-prime?
- Why?
๐ Case Study 3: Puzzle
A pair has HCF = 1
- What are such numbers called?
- Give one example
๐ Case Study 4: Consecutive Numbers
- Are 20 and 21 co-prime?
- Give reason
๐ Case Study 5: Number Challenge
- Write two co-prime numbers between 10 and 20
- Write two co-prime odd numbers
- Write two co-prime even numbers (if possible)
- Write one co-prime pair where both are composite
- Write one co-prime pair where one is prime and one is composite
- Find HCF of 13 and 27
- Are 13 and 27 co-prime?
- Find HCF of 16 and 18
- Are they co-prime?
- Write two consecutive co-prime numbers
- Write smallest co-prime pair
โ ANSWER KEY
SECTION A
- 1
- Yes
- No
- Yes
- Yes
- No
- Example: 8 and 15
- 1
- Yes
- No
SECTION B
- Co-prime
- Not
- Co-prime
- Co-prime
- Not
- Co-prime
- Co-prime
- Co-prime
- Not
- Co-prime
SECTION C
- 1
- 1
- 1
- 6
- 1
SECTION D
- Yes
- No (except 2 and 4? โ still not)
- Yes
- Yes
- (6,7)
SECTION E
- (4,5), (5,6), (6,7), (5,7)
- Any two pairs above
- 1
- Yes
- Only common factor is 1
- Co-prime numbers
- Example: 7 and 8
- Yes
- Consecutive numbers
- Example: 11 and 12
- Example: 9 and 11
- Not possible (except trivial cases)
- Example: 8 and 15
- Example: 7 and 8
- 1
- Yes
- 2
- No
- Example: 15 and 16
- 1 and 2
