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?

["The Greatest Common Factor of 72g, 108g, and 180g: Finding the Largest Uniform Container Size for Space Crystal Collection", "When a space explorer ventures beyond the known planets, collecting precious crystals from celestial bodies, a critical question arises: what is the largest uniform container size that can exactly measure the weights of each crystal gathered? In the case of a space explorer who collected 72 grams, 108 grams, and 180 grams of crystals from three moons, the answer lies in calculating the Greatest Common Factor (GCF) — also called the Greatest Common Divisor (GCD).", "The GCF is the largest number that divides each weight without leaving a remainder — representing the heaviest container unit that fits perfectly into every collected sample. This solution ensures efficient packaging, resource tracking, and balanced distribution in space missions or interplanetary science labs.", "### The Weights Collected\n- Moon 1: 72 grams\n- Moon 2: 108 grams\n- Moon 3: 180 grams", "To find the GCF, we determine the prime factors of each weight:", "- 72\n (72 = 2^3 \ imes 3^2)", "- 108\n (108 = 2^2 \ imes 3^3)", "- 180\n (180 = 2^2 \ imes 3^2 \ imes 5)", "Now, identify the common prime factors with the lowest exponents across all three factorizations:\n- The common prime bases are 2 and 3.\n- For 2: minimum exponent is (2^2)\n- For 3: minimum exponent is (3^2)\n- The factor 5 appears only in 180, so it’s excluded.", "Thus, multiply these together:\n[\nGCF = 2^2 \ imes 3^2 = 4 \ imes 9 = 36\n]", "### What Does This Mean for the Space Explorer?\nThe greatest common factor of 72, 108, and 180 grams is 36 grams. This means:", "- Each crystal weight is perfectly divisible by 36 grams.\n- The largest uniform container size that can measure each amount exactly is 36 grams.\n- The explorer can pack samples into containers holding 36g each — simplifying storage, transport, and inventory management across space stations or research facilities.", "---", "This mathematical insight demonstrates how number theory enhances practical space exploration, enabling efficient handling of extraterrestrial materials. Whether cataloging alien minerals or planning cargo logistics, identifying the GCF ensures precision and efficiency in every mission phase.", "Keywords: GCF of 72, 108, 180, greatest common factor, space exploration, crystal container size, prime factorization, space mission logistics, unified measuring unit.", "---", "Understanding math in space not only satisfies curiosity but strengthens future interplanetary science and resource management."]