If the GCD of two numbers is 1, which of the following statements is true?

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Question: If the GCD of two numbers is 1, which of the following statements is true?

Options:

Correct Answer: The numbers are co-prime

Solution:

If the GCD of two numbers is 1, it means they have no common factors other than 1, hence they are co-prime.

If the GCD of two numbers is 1, which of the following statements is true?

If the GCD of two numbers is 1, which of the following statements is true?

Step 1: Understand what GCD means. GCD stands for Greatest Common Divisor, which is the largest number that divides two numbers without leaving a remainder.
Step 2: Know what it means for the GCD to be 1. If the GCD of two numbers is 1, it means that the only number that can divide both of them evenly is 1.
Step 3: Recognize the term 'co-prime'. Two numbers are called co-prime if their GCD is 1.
Step 4: Conclude that if the GCD of two numbers is 1, then they are co-prime, meaning they do not share any common factors other than 1.

Greatest Common Divisor (GCD) – The largest positive integer that divides two or more integers without leaving a remainder.
Co-prime Numbers – Two integers are co-prime if their GCD is 1, meaning they have no common factors other than 1.