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"Flowers to Wake Up To: The Ultimate Good Morning Floral Boost! - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 To maximize \(\gcd(a, b)\), we note that if \(\gcd(a, b) = d\), then \(a = dx\) and \(b = dy\) for some integers \(x\) and \(y\) with \(\gcd(x, y) = 1\). Thus, \(a + b = dx + dy = d(x + y) = 2023\). Therefore, \(d\) must divide 2023.

📌 First, we factor 2023 to find its divisors. Checking small prime numbers:

📌 2023 is odd, so not divisible by 2.

📌 Sum of digits of 2023 is \(2+0+2+3 = 7\), not divisible by 3.

📌 2023 does not end in 0 or 5, so not divisible by 5.

📌 Check divisibility by 7: \(2023 \div 7 \approx 289.0\), and \(7 \times 289 = 2023\), so 2023 is divisible by 7.

📌 Now, factor 289:

📌 \(\sqrt{289} = 17\), and \(17 \times 17 = 289\).

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