Canonical Polyadic Decomposition (CPD), also known as PARAFAC, is a useful tool for tensor factorization. It has found application in several domains including signal processing and data mining. With the deluge of data faced in our societies, large-scale matrix and tensor factorizations become a crucial issue. Few works have been devoted to large-scale tensor factorizations. In this paper, we introduce a fully distributed method to compute the CPD of a large-scale data tensor across a network of machines with limited computation resources. The proposed approach is based on collaboration between the machines in the network across the three modes of the data tensor. Such a multi-modal collaboration allows an essentially unique reconstruction of the factor matrices in an efficient way. We provide an analysis of the computation and communication cost of the proposed scheme and address the problem of minimizing communication costs while maximizing the use of available computation resources.