Class 6 Exam > Class 6 Questions > Which of these pairs of numbers are co-prime?...
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Which of these pairs of numbers are co-prime?
- a)8 and 12
- b)14 and 21
- c)9 and 28
- d)15 and 20
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Which of these pairs of numbers are co-prime?a)8 and 12b)14 and 21c)9 ...
Co-prime numbers have no common factors other than 1. 9 and 28 are co-prime because they have no common factors other than 1.
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Which of these pairs of numbers are co-prime?a)8 and 12b)14 and 21c)9 ...
Understanding Co-prime Numbers
Co-prime numbers, also known as relatively prime numbers, are pairs of numbers that have no common factors other than 1. This means their greatest common divisor (GCD) is 1.
Analyzing Each Pair
Let's examine each pair of numbers to determine if they are co-prime:
a) 8 and 12
- Factors of 8: 1, 2, 4, 8
- Factors of 12: 1, 2, 3, 4, 6, 12
- Common factors: 1, 2, 4
- GCD: 4
- Conclusion: Not co-prime.
b) 14 and 21
- Factors of 14: 1, 2, 7, 14
- Factors of 21: 1, 3, 7, 21
- Common factors: 1, 7
- GCD: 7
- Conclusion: Not co-prime.
c) 9 and 28
- Factors of 9: 1, 3, 9
- Factors of 28: 1, 2, 4, 7, 14, 28
- Common factor: 1
- GCD: 1
- Conclusion: Co-prime!
d) 15 and 20
- Factors of 15: 1, 3, 5, 15
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 5
- GCD: 5
- Conclusion: Not co-prime.
Final Conclusion
Among the pairs provided, only 9 and 28 are co-prime numbers because they share no common factors other than 1. This makes option C the correct answer.
Co-prime numbers, also known as relatively prime numbers, are pairs of numbers that have no common factors other than 1. This means their greatest common divisor (GCD) is 1.
Analyzing Each Pair
Let's examine each pair of numbers to determine if they are co-prime:
a) 8 and 12
- Factors of 8: 1, 2, 4, 8
- Factors of 12: 1, 2, 3, 4, 6, 12
- Common factors: 1, 2, 4
- GCD: 4
- Conclusion: Not co-prime.
b) 14 and 21
- Factors of 14: 1, 2, 7, 14
- Factors of 21: 1, 3, 7, 21
- Common factors: 1, 7
- GCD: 7
- Conclusion: Not co-prime.
c) 9 and 28
- Factors of 9: 1, 3, 9
- Factors of 28: 1, 2, 4, 7, 14, 28
- Common factor: 1
- GCD: 1
- Conclusion: Co-prime!
d) 15 and 20
- Factors of 15: 1, 3, 5, 15
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 5
- GCD: 5
- Conclusion: Not co-prime.
Final Conclusion
Among the pairs provided, only 9 and 28 are co-prime numbers because they share no common factors other than 1. This makes option C the correct answer.
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Which of these pairs of numbers are co-prime?a)8 and 12b)14 and 21c)9 and 28d)15 and 20Correct answer is option 'C'. Can you explain this answer?
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