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\[ k = 2h - 4 \] - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Question: A space explorer collects crystals from three moons, each yielding weights of 72 grams, 108 grams, and 180 grams. What is the greatest common factor of these weights, representing the largest uniform container size (in grams) that can measure each exact amount?

📌 Solution: We find $ \gcd(72, 108, 180) $.

📌 First, factor each number:

📌 $ 72 = 2^3 \cdot 3^2 $

📌 $ 108 = 2^2 \cdot 3^3 $

📌 $ 180 = 2^2 \cdot 3^2 \cdot 5 $

📌 Take the lowest powers of common primes:

📌 $ 2^2 $ and $ 3^2 $

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