Journal article: We study linear factor models under the assumptions that factors are mutually independent and independent of errors, and errors can be correlated to some extent. Under the factor non-Gaussianity, second-to-fourth-order moments are shown to yield full identification of the matrix of factor loadings. We develop a simple algorithm to estimate the matrix of factor loadings from these moments. We run Monte Carlo simulations and apply our methodology to data on cognitive test scores, and financial data on stock returns.