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Home » Now compute $3025 \mod 9$. Use the digit sum method: - Carbonext

Now compute $3025 \mod 9$. Use the digit sum method: - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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

📌 Let the three consecutive integers be \(n\), \(n+1\), and \(n+2\). The product is \(n(n+1)(n+2)\). Among any three consecutive integers, at least one is divisible by 2 and at least one is divisible by 3. Therefore, the product is divisible by \(2 \times 3 = 6\).

📌 To see if a larger number must divide the product, consider the following cases:

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