We propose a new model for volatility forecasting which combines the Generalized Dynamic Factor Model (GDFM) and the GARCH model. The GDFM, applied to a large number of series, captures the multivariate information and disentangles the common and the idiosyncratic part of each series of returns. In this financial analysis, both these components are modeled as a GARCH.We compare GDFM+GARCH and standard GARCH performance on two samples up to 171 series, providing one-step-ahead volatility predictions of returns. The GDFM+GARCH model outperforms the standard GARCH in most cases. These results are robust with respect to different volatility proxies.