COBRA (Cosmology with Optimally factorized Bases for Rapid Approximation) rapidly computes large-scale structure observables, separating scale dependence from cosmological parameters in the linear matter power spectrum while also minimizing the number of necessary basis terms. This enables direct and efficient computation of derived and nonlinear observables. Moreover, the dependence on cosmological parameters is efficiently approximated using radial basis function interpolation. COBRA opens a new window for efficient computations of higher loop and higher order correlators involving multiple powers of the linear matter power spectra. The resulting factorization can also be utilied in clustering, weak lensing and CMB analyses.