Multi-view clustering is a popular unsupervised multi-view learning method. Real-world multi-view data are often distributed across multiple entities, presenting a challenge for performing multi-view clustering. Federated learning provides a solution by enabling multiple entities to collaboratively train a global model. However, existing federated multi-view clustering methods usually conduct feature extraction and clustering in separate steps, potentially leading to a degradation in clustering performance. To address this issue and for the sake of efficiency, we propose a novel Federated Multi-View Clustering method with Integrated Matrix Factorization and K-Means (FMVC-IMK), which integrates matrix factorization and multi-view K-means into one step. Additionally, an adaptive weight is employed to balance the influence of data from each view. FMVC-IMK further incorporates a graph-based regularizer to preserve the original data's geometric structure within the learned global clustering structure. We also develop a federated optimization approach to collaboratively learn a global clustering result without sharing any original data. Experimental results on multiple datasets demonstrate the effectiveness of FMVC-IMK.