The possible mechanisms for the synchronization of rest-activity rhythms of individual animals living in groups is a relatively understudied question; synchronized rhythms could occur by entrainment of individuals to a common external force and/or by social synchronization between individuals. To gain insight into this question, we explored the synchronization dynamics of populations of globally coupled Kuramoto oscillators and analyzed the effects of a finite oscillator number (N) and the variable strengths of their periodic forcing (F) and mutual coupling (K). We found that increasing N promotes entrainment to a decreasing value of F, but that F could not be reduced below a certain level determined by the number of oscillators and the distribution width of their intrinsic frequencies. Our analysis prompts some simple predictions of ecologically optimal animal group sizes under differing natural conditions.