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What is the H.C.F. of two co-prime numbers?
- a)1
- b)0
- c)2
- d)Their product
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the H.C.F. of two co-prime numbers?a)1b)0c)2d)Their productCor...
Co-prime numbers have no common factor other than 1. So, their H.C.F is 1.
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What is the H.C.F. of two co-prime numbers?a)1b)0c)2d)Their productCor...
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 highest common factor (H.C.F.) is 1.
Definition of H.C.F.
- The H.C.F. of two or more numbers is the largest number that divides all of them without leaving a remainder.
- For co-prime numbers, the only number that divides both is 1.
Why is the H.C.F. 1?
- Since co-prime numbers do not share any prime factors, the only divisor they both share is 1.
- For example, consider the numbers 8 and 15:
- The factors of 8: 1, 2, 4, 8
- The factors of 15: 1, 3, 5, 15
- The only common factor is 1.
Examples of Co-Prime Numbers
- 3 and 4: Factors are {1, 3} and {1, 2, 4}. H.C.F. = 1
- 7 and 9: Factors are {1, 7} and {1, 3, 9}. H.C.F. = 1
- 10 and 21: Factors are {1, 2, 5, 10} and {1, 3, 7, 21}. H.C.F. = 1
Conclusion
Since co-prime numbers only share the factor 1, the H.C.F. of any two co-prime numbers is always 1. Thus, the correct answer to the question is option 'A'.
Co-prime numbers, also known as relatively prime numbers, are pairs of numbers that have no common factors other than 1. This means their highest common factor (H.C.F.) is 1.
Definition of H.C.F.
- The H.C.F. of two or more numbers is the largest number that divides all of them without leaving a remainder.
- For co-prime numbers, the only number that divides both is 1.
Why is the H.C.F. 1?
- Since co-prime numbers do not share any prime factors, the only divisor they both share is 1.
- For example, consider the numbers 8 and 15:
- The factors of 8: 1, 2, 4, 8
- The factors of 15: 1, 3, 5, 15
- The only common factor is 1.
Examples of Co-Prime Numbers
- 3 and 4: Factors are {1, 3} and {1, 2, 4}. H.C.F. = 1
- 7 and 9: Factors are {1, 7} and {1, 3, 9}. H.C.F. = 1
- 10 and 21: Factors are {1, 2, 5, 10} and {1, 3, 7, 21}. H.C.F. = 1
Conclusion
Since co-prime numbers only share the factor 1, the H.C.F. of any two co-prime numbers is always 1. Thus, the correct answer to the question is option 'A'.
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What is the H.C.F. of two co-prime numbers?a)1b)0c)2d)Their productCorrect answer is option 'A'. Can you explain this answer?
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What is the H.C.F. of two co-prime numbers?a)1b)0c)2d)Their productCorrect answer is option 'A'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about What is the H.C.F. of two co-prime numbers?a)1b)0c)2d)Their productCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the H.C.F. of two co-prime numbers?a)1b)0c)2d)Their productCorrect answer is option 'A'. Can you explain this answer?.
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