This paper develops multi-factor copula models to capture the time-varying dependence across a large panel of financial assets. The factor structures are based on group characteristics of financial assets, which allows for different patterns of within and between group dependencies. We build score-driven dynamics for the factor loadings, possibly driven by exogenous variables. The factor copula model retains computational tractable as the copula density is available in closed form, which proves beneficial for parameter estimation. We apply our new approach to daily equity returns, realized variances and realized equi-correlations of 100 stocks of the S&P 500 index over the period 2001 to 2014. One-step ahead copula-density forecasts of the whole support and in the joint lower tail based on multi-factor copula models significantly improve upon one-factor models and recently developed benchmarks. Finally, including realized measures into the factor copula specification statistically improves the density forecasts, although the influence vanishes when the factor structure enriches.