The highest common factor of a set of coprime numbers is equal to:

Question

Examoogle · Accepted Answer

The correct answer is Option A: 1. By definition, coprime numbers (or relatively prime numbers) are integers that share no common factors other than 1. Therefore, their Highest Common Factor (HCF) or Greatest Common Divisor (GCD) is always 1.

Step-by-Step Solution & Concepts:
Shortcut Trick: By definition, coprime numbers (or relatively prime numbers) are integers that share no common factors other than 1. Therefore, their Highest Common Factor (HCF) or Greatest Common Divisor (GCD) is always 1.

Formula Used: $$HCF(a, b) = 1 \ ext{ for coprime } a, b$$

Given: A set of numbers defined as 'coprime' numbers.

Steps: Define Coprime Numbers: A set of numbers $a$ and $b$ is called coprime if their only common divisor is 1.. Evaluate HCF: The Highest Common Factor (HCF) is synonymous with the Greatest Common Divisor (GCD). By the definition of coprime integers, the greatest factor that divides all numbers in the set is 1.. Verification: For any set of coprime numbers $\{a_1, a_2, ..., a_n\}$, the condition is that no integer greater than 1 divides all elements of the set.

Answer: A is correct because by definition, coprime numbers share no common factors other than 1, making their HCF equal to 1.

Exam Tip: Understanding coprimality is essential for simplifying fractions and working with modular arithmetic in competitive exams, as it helps determine if a fraction is in its irreducible form.

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