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Home » \(8x = 32\) â \(x = rac328 = 4\). - Red Crowns

\(8x = 32\) â \(x = rac328 = 4\). - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 But test $ 1\cdot2\cdot3\cdot4 = 24 $ → divisible by 24

📌 $ 2\cdot3\cdot4\cdot5 = 120 $, divisible by 24

📌 $ 3\cdot4\cdot5\cdot6 = 360 $, $ 360 / 24 = 15 $

📌 Is 48 always a divisor? $ 24 $ is not divisible by 48 → no

📌 So maximum guaranteed divisor is 24.

📌 Thus, the largest integer that must divide the product is $ \boxed{24} $.

📌 Question: What is the remainder when $ 2023^2 + 2024^2 + 2025^2 $ is divided by 6?

📌 Solution: We compute modulo 6. Note that $ 2023 \equiv 1 \pmod{6} $, $ 2024 \equiv 2 \pmod{6} $, $ 2025 \equiv 3 \pmod{6} $.

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