We present a simple macroeconomic model with a continuum of primary commodities used in the production of the final good, such that the real prices of commodities have a factor structure. One factor captures the combined contribution of all aggregate shocks which have no direct effects on commodity markets other than through general equilibrium effects on output, while other factors represent direct commodity shocks. Thus, the factor structure provides a decomposition of underlying structural shocks. The theory also provides guidance on how empirical factors can be rotated to identify the structural factors. We apply factor analysis and the identification conditions implied by the model to a cross-section of real non-energy commodity prices. The theoretical restrictions implied by the model are consistent with the data and thus yield a structural interpretation of the common factors in commodity prices. The analysis suggests that commodity-related shocks have generally played a limited role in global business cycle fluctuations.