Symmetric Matrices & Quadratic Forms · Superchallenge problem

Consider the quadratic form $Q(x_1, \ldots, x_8) = \displaystyle\sum_{i=1}^{8}\sum_{j=1}^{8}\gcd(i, j)\,x_ix_j$. Find the determinant of its $8\times 8$ matrix $G = (\gcd(i, j))$.