What is the highest common factor of two coprime numbers?
Answer and explanation
Correct answer: 1
The governing concept is the definition of coprime, or relatively prime, numbers. Two integers are called coprime when their only positive common factor is 1. Therefore their highest common factor, also called greatest common divisor, is 1. Option C is correct. The numbers themselves need not be prime: for example, 8 and 15 are both composite in the broad sense of ordinary integers, yet their common factors include only 1, so HCF(8,15) = 1. A value of 2 or 3 would mean that both numbers share that factor, which would contradict coprimality. Zero is not the HCF of ordinary nonzero coprime numbers. This property is important in rational-number proofs because a fraction in lowest form has a numerator and denominator whose HCF is 1.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The governing concept is the definition of coprime, or relatively prime, numbers. Two integers are called coprime when their only positive common factor is 1. Therefore their highest common factor, also called greatest common divisor, is 1. Option C is correct. The numbers themselves need not be prime: for example, 8 and 15 are both composite in the broad sense of ordinary integers, yet their common factors include only 1, so HCF(8,15) = 1. A value of 2 or 3 would mean that both numbers share that factor, which would contradict coprimality. Zero is not the HCF of ordinary nonzero coprime numbers. This property is important in rational-number proofs because a fraction in lowest form has a numerator and denominator whose HCF is 1.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Rational numbers.
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