2Dr. Liam Chen, an anthropologist, is analyzing tool usage across five ancient communities. Each community used a different set of tools: Community A used 24 tools, B used 36, C used 48, D used 60, and E used 72. He wants to group them into equal-sized research teams such that each team studies the same total number of tools. What is the maximum number of tools each team can study if every community’s tools must remain intact?

["Maximizing Research Efficiency: Finding the Largest Equal Team Size Across Ancient Tool Sets", "In an innovative study bridging archaeology and anthropology, Dr. Liam Chen, an anthropologist, is examining tool usage across five ancient communities to uncover patterns of cooperation and knowledge sharing. Community A used 24 tools, Community B used 36 tools, Community C used 48 tools, Community D used 60 tools, and Community E used 72 tools. Dr. Chen aims to divide the total tools of each community into research teams such that every team studies the same total number of tools—without splitting any community’s tool set. What is the maximum number of tools each research team can analyze?", "To solve this, Dr. Chen must determine the largest number that divides evenly into the total number of tools from all communities. In mathematical terms, he seeks the greatest common divisor (GCD) of the five tool counts: 24, 36, 48, 60, and 72.", "Let’s compute the GCD step by step:", "- First, factor each number:\n - 24 = (2^3 \ imes 3)\n - 36 = (2^2 \ imes 3^2)\n - 48 = (2^4 \ imes 3)\n - 60 = (2^2 \ imes 3 \ imes 5)\n - 72 = (2^3 \ imes 3^2)", "- Identify the lowest power of each common prime factor:\n - For prime (2): minimum exponent is 2 → (2^2 = 4)\n - For prime (3): minimum exponent is 1 → (3^1 = 3)\n - The prime 5 appears in only 60, so it is not included", "- Multiply these together:\n (2^2 \ imes 3 = 4 \ imes 3 = 12)", "Thus, the GCD of 24, 36, 48, 60, and 72 is 12.", "This means the maximum number of tools each team can study—while keeping full tool sets intact and balancing workload across communities—is 12 tools per team.", "For example:\n- Community A: 24 tools ÷ 2 teams = 12 each\n- Community B: 36 ÷ 3 teams = 12 each\n- Community C: 48 ÷ 4 = 12\n- Community D: 60 ÷ 5 = 12\n- Community E: 72 ÷ 6 = 12", "Each team studies exactly 12 tools, and no community’s tools are split.", "This elegant mathematical insight allows Dr. Chen to standardize team size across diverse ancient cultures, enabling meaningful comparative analysis while preserving the integrity of original archaeological datasets.", "📌 Key Takeaway: By finding the GCD of tool counts, researchers can assign optimal, balanced study teams—proving that even in ancient times, collaboration prioritized common ground.", "Whether studying tool complexity, social organization, or technological evolution, tools like Dr. Chen’s analysis help unlock deeper truths about human ingenuity across ages."]