Detecting whether a news article is fake or genuine is a crucial task in today's digital world where it's easy to create and spread a misleading news article. This is especially true of news stories shared on social media since they don't undergo any stringent journalistic checking associated with main stream media. Given the inherent human tendency to share information with their social connections at a mouse-click, fake news articles masquerading as real ones, tend to spread widely and virally. The presence of echo chambers (people sharing same beliefs) in social networks, only adds to this problem of wide-spread existence of fake news on social media. In this paper, we tackle the problem of fake news detection from social media by exploiting the very presence of echo chambers that exist within the social network of users to obtain an efficient and informative latent representation of the news article. By modeling the echo-chambers as closely-connected communities within the social network, we represent a news article as a 3-mode tensor of the structure - <News, User, Community> and propose a tensor factorization based method to encode the news article in a latent embedding space preserving the community structure. We also propose an extension of the above method, which jointly models the community and content information of the news article through a coupled matrix-tensor factorization framework. We empirically demonstrate the efficacy of our method for the task of Fake News Detection over two real-world datasets. Further, we validate the generalization of the resulting embeddings over two other auxiliary tasks, namely: \textbf{1)} News Cohort Analysis and \textbf{2)} Collaborative News Recommendation. Our proposed method outperforms appropriate baselines for both the tasks, establishing its generalization.