Yaravam ben Navat was from Efrayim. In Sanhedrin (101b) it says that Navat, Michah and Sheva ben Bichri are the same. Sheva ben Bichri was from Binyamin!
Maharsha (101b): Also Michah and Sheva ben Bichri were "me'Har Efrayim 1 " (Shoftim 17:1, Shmuel II, 20:21).
Maris ha'Ayin (the Chida; 101b): They were Gilgulim of one another (refer to Shoftim 3:8:1:1*).
Maharsha does not explain why Sheva ben Bichri is called "Ish Yemini" (Shmuel II, 20:1). Presumably, this is why Radak left this difficult. Me'Har Efrayim means that he lived there, but not that he was from Shevet Efrayim. Many Midrashim say that Michah was from Dan. Elkanah was from Har Efrayim (Shmuel I, 1:1), and he was a Levi! (PF) Be'er Sheva (101b) and Yashresh Yakov asked also how this Rasha could live so long. The Chida answered also this (refer to 11:26:1:2).
What is the meaning of "Efrati"?
Radak: He was from Shevet Efrayim.
Why does it mention that his mother was a widow?
Malbim: Even so, and even though he was a servant of Shlomo, he rebelled against him.
What is the meaning of "va'Yarem Yad ba'Melech"?
Rashi (from Sanhedrin 101b): He publicly rebuked him (refer to 11:27:2:1,2. Radak - he merited kingship for rebuking him, but was punished for rebuking him in public.
Malbim: He rebelled against him; Radak - also, he did not fear him.
Why did Yaravam rebel against Shlomo?
Radak: Shlomo had appointed him to receive the tax from Menasheh and Efrayim, for he saw that he is zealous in his work (verse 28). The Navi Achiyah ha'Shiloni told him that he will be king. He became haughty, and said what he said about Shlomo. When Shlomo heard, he tried to kill him; Yaravam fled to Egypt. The Navi is out of order; it puts in the middle the reason he became haughty.
