Given that 6 is the greatest common divisor of two positive integers a and b, what is the greatest common divisor of 4a and 4b?

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Official Explanation

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Since 6 is the greatest common divisor of the positive integers a and b, it means that 6 is a common factor of both a and b, and there are no other common factors greater than 6. To find the greatest common divisor…

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Comments

ShubhankarNov 24, 2024

Can someone explain it other way?

IFeb 12, 2024

Thankss

JonasJun 23

Wait, why isn't the answer just 4 times 6? Is it because 4 and 6 share factors? I keep second-guessing myself here lol

UthejJul 6

Yeah that's exactly the trap. Multiplying both numbers by 4 doesn't just multiply the gcd by 4 if 4 and 6 overlap — you have to account for the shared factor.

What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.