Sكية: The greatest common divisor of $a$ and $b$ must divide their sum, which is 2025. To maximize $\gcd(a,b)$, we find the largest proper divisor of 2025. Factoring 2025: $2025 = 3^4 \times 5^2$. The largest proper divisor is $2025 / 3 = 675$. Thus, the maximum $\gcd(a,b)$ is $\boxed675$. - Nelissen Grade advocaten