A denominator is a name. The word is closely related to the word nominate, to name a person for public office. The most common use of the word today is for the part of a fraction that tells how many equal parts make up a whole, and which is used in the name of the fraction: "halves", "thirds", "fourths" or "quarters", "fifths" and so on. In the fraction , 4 is the denominator and the name of the fraction is "three fourths". Nomination is part of the process of selecting a candidate for either election to an office, or the bestowing of an honor or award. ... A cake divided into four equal quarters. ...
Denominations usually have a significant degree of authority over their member congregations, although the term is also used to describe religious groups when the congregations have authority over the "denomination", such as the numerous Baptist associations or the Unitarian Universalist Association.
Denominations often form slowly over time for many reasons; due to historical accidents of geography, culture, and influence between different groups, members of a given religion slowly begin to diverge in their views.
In other cases, denominations form very rapidly, either as a result from a split or schism in an existing denomination, or as people from many different denominations share an experience of spiritual revival or spiritual awakening, and choose to form a new denomination based on that new experience or understanding.
Pastors who differ with their denomination theologically tend to be split almost evenly between those who feel the denomination is too liberal and those who believe it is too conservative.
Interestingly, while mainline denominations tend to be more theologically liberal and evangelical denominations tend to be more theologically conservative, how pastors from each group perceive the denominations they're in does not differ much between the two groups.
And while we can't say that every denomination is a good theological match with the ministers serving in that denomination, when viewed in the big picture, it's hard to see where a change could improve things.