At the end of the Jin Dynasty, there were indeed six ministers who held real power. But it was indeed three that caused the jin state to perish and divide the jin state. Three other homes were wiped out.
At the end of the Spring and Autumn Period, that is, at the end of the Jin Dynasty, there were actually seven forces: Han, Zhao, Wei, Zhi, Fan, the Six Qings of the Zhongxing Clan, and the Jin State Emperor Jin Pinggong.
Among these seven families, the strength of the Duke of Jinping, or the king of the Jin Dynasty, was the weakest. The other six secretaries are all powerful. However, the six secretaries are not united and monolithic, but full of contradictions and mutual inclination.
In this process, to put it simply, Zhao destroyed the Fan and Zhonghang families, and then united with Han and Wei to eliminate the Zhi clan. The six secretaries became the three secretaries. None of these actions were approved by The Duke of Jinping, and the objections of the Duke of Jinping were null and void. The Jin Dynasty has already died in name only.
403 BC, keep in mind this year, it is an important time node in Chinese history. During this year, King Weilie of Zhou enfeoffed the three families of Zhao, Wei, and Han as princes.
At the beginning of the establishment of the Zhou Dynasty, "under the whole world, there is no royal land", and the king of Zhou could divide any piece of land to the princes. However, by the end of the Spring and Autumn Period, the King of Zhou had no land in his direct control to divide and seal. Therefore, the fiefdom given to Zhao Weihan was actually the Jin Gong land they had encroached upon.
In other words, the Zhou King's division of the three families of Zhao Wei and Han actually acknowledged their status as "Qing Dafu" and the encroachment on the Jin state office. This matter is generally regarded as the boundary between the Spring and Autumn Period and the Warring States.
Strictly speaking, at this time, the Jin state was divided into four kingdoms: Jin, Zhao, Wei, and Han, and Jin was the weakest of them. But this situation did not last long. In 376 BC, Han, Zhao, and Wei deposed the Duke of Jin and divided up the remaining land of the Jin dynasty. The jin state that was once weihe was completely divided into three countries.
History is called "three families divided into Jin".
The three kingdoms of Zhao, Wei, and Han were all differentiated from the Jin state, so they were collectively called "three Jin". This is also the origin of Shanxi's reputation as the "Three Jins".