Solution: The greatest common divisor of $a$ and $b$ must divide their sum $a + b = 100$. The largest divisor of 100 is 50. To achieve $\gcd(a, b) = 50$, set $a = 50$ and $b = 50$. Thus, the maximum value is $oxed{50}$.

Tue, 05 May 2026 16:59:16 +0000

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