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Home » These Crazy Would You Rather Questions Will Change Your Life Forever! - Ready Digital AB

These Crazy Would You Rather Questions Will Change Your Life Forever! - Ready Digital AB

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 Thus, the possible answers are $ \boxed{43} $ and $ \boxed{78} $.

📌 Question: What is the largest integer that must divide the product of any four consecutive integers?

📌 Solution: Let the four consecutive integers be $ n, n+1, n+2, n+3 $. Their product is $ n(n+1)(n+2)(n+3) $.

📌 We analyze divisibility properties:

📌 Among any four consecutive integers, at least one is divisible by 4.

📌 At least two are even, so the product is divisible by $ 2 \cdot 2 = 4 $.

📌 At least one is divisible by 3.

📌 Therefore, the product is divisible by $ 4 \cdot 2 \cdot 3 = 24 $.

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