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The Internet of Things (IoT) extends Internet connectivity to resource-constrained devices such as sensors and actuators. It is prone to several security threats and attacks, due to which defence mechanisms such as encryption, message authentication codes, authentication, etc., need to be employed. Several IoT scenarios require secure communication to and data acquisition from multiple devices, which constitute a “group”. Also, in dynamic IoT scenarios, devices join or leave a group from time to time, due to which the group keys, which are used for multicasting information within the group, need to be efficiently updated. We propose a novel scheme, based on factorial trees and the Chinese Remainder Theorem, for efficient Group Key Management. Our proposed scheme prevents malicious users from accessing information from a group and efficiently updates the group keys when devices join or leave a group, while guaranteeing forward and backward secrecy. We evaluate the performance of the proposed scheme via extensive mathematical analysis and numerical computations, and show that it outperforms schemes proposed in prior work in terms of the communication and computation costs incurred by IoT devices.