Synchronized Random Access Channel (RACH) attempts by Internet of Things (IoT) devices could result in Radio Access Network (RAN) overload in LTE-A. 3GPP adopted Barring Bitmap Enabled-Extended Access Barring (EAB-BB) mechanism that announces the EAB information (i.e., a list of barred Access Classes) through a barring bitmap as the baseline solution to mitigate the RAN overload. EAB-BB was analyzed for its optimal performance in a recent work. However, there has been no work that analyzes Barring Factor Enabled-Extended Access Barring (EAB-BF), an alternative mechanism that was considered during the standardization process. Due to the modeling complexity involved, not only has it been difficult to analyze EAB-BF, but also, a much more far-reaching issue, like the effect of these schemes on key network performance parameter, like eNodeB energy consumption, has been overlooked. In this regard, for the first time, we develop a novel analytical model for EAB-BF to obtain its performance metrics. Results obtained from our analysis and simulation are seen to match very well. Furthermore, we also build an eNodeB energy consumption model to serve the IoT RACH requests. We then show that our analytical and energy consumption models can be combined to obtain EAB-BF settings that can minimize eNodeB energy consumption, while simultaneously providing optimal Quality of Service (QoS) performance. Results obtained reveal that the optimal performance of EAB-BF is better than that of EAB-BB. Furthermore, we also show that not only all the three 3GPP-proposed EAB-BF settings considered during standardization provide sub-optimal QoS to devices, but also result in excessive eNodeB energy consumption, thereby acutely penalizing the network. Finally, we provide corrections to these 3GPP-settings that can lead to significant gains in EAB-BF performance.