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Home » Bold Front Porch Designs That Will Zoom Your Home’s Curb Appeal! - Databee Business Systems

Bold Front Porch Designs That Will Zoom Your Home’s Curb Appeal! - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \gcd(2^{12} - 1, 2^{18} - 1) = 2^6 - 1 = 64 - 1 = 63

📌 Therefore, the greatest common divisor is $ \boxed{63} $.

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

📌 Solution: Let the four consecutive integers be $ n, n+1, n+2, n+3 $.

📌 Among any four consecutive integers:

📌 There are at least two even numbers, and one of them is divisible by 4 → total factor of $ 2^3 = 8 $

📌 There is exactly one multiple of 4 and another even, so $ 8 \mid $ product

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

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