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nascar iowa speedway - Richter Guitar

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Factor $2024$:

📌 = 2^3 imes 11 imes 23.

📌 So the largest divisor is $2024$ itself, but for $d = 2024$, we would need $a = 2024$, $b = 0$, but $b$ must be positive â invalid.

📌 Try the next largest divisor: $1012 = 2024/2$. Can we have $a = 1012$, $b = 1012$? Then $a + b = 2024$, both even, and $\gcd(1012,1012) = 1012$.

📌 So $d = 1012$ is achievable.

📌 Now verify if a larger $d$ is possible: no divisor of $2024$ larger than $1012$ divides $2024$ and allows both $a$ and $b$ positive and even.

📌 Hence, the maximum $\gcd$ is $1012$.

📌 Therefore, the largest possible value is $oxed{1012}$.

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