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Home » 12^2 = 144 < 200 - Ready Digital AB

12^2 = 144 < 200 - Ready Digital AB

📅 March 8, 2026 👤 scraface

Mar 08, 2026

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📌 There is at least one multiple of 3 → $ 3 \mid $ product

📌 There is no guaranteed factor of 5 or higher

📌 So the product is always divisible by $ 8 \cdot 3 = 24 $. But can we do better?

📌 Check more precisely:

📌 The product includes:

📌 At least one multiple of 3 → $ 3 $

📌 At least three factors of 2: among four consecutive numbers, the even numbers contribute at least $ 2 + 1 = 3 $ factors of 2 (e.g., 2 and 4 give $ 2^1 $ and $ 2^2 $).

📌 Additionally, among four consecutive numbers, one is divisible by 4, and another even → total $ 2^3 = 8 $

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