Given that \( x + y = 100 \), we aim to find the largest possible \(\gcd(x, y)\). Let \( d = \gcd(x, y) \). Then \( x = dm \) and \( y = dn \) for some integers \( m \) and \( n \) such that \(\gcd(m, n) = 1\). Substituting into the sum, we have: - Nelissen Grade advocaten