Each, other, everyone, either and neither are distributive pronouns, as they separate one person or a thing from a group of persons or things. They always take singular verb.
Each of them was a player.
Either of the two boys was required but neither of the two was ready.
Either of you can go.
Each took it in a turn.
When number of persons or things are taken singly than each is used to denote everyone.
Either means the first of the second one.
Neither means not the first and not the second one.
Hence either and neither should be used only when we speak of two persons or things.
When we talk about separation of more than two persons or things than any,none should be used.
NOTE:- Each , either and neither ca be used as adjectives. Here they are followed by nouns (Singular in number).
Each girl took her turn.
At either end was a gate.
Either of the boy received a reward.
Each cow cost 50,000 rupees.
LOOK AT THE FOLLOWING SENTENCES
The two women hate each other.
They cheated one another.
If we analyse them thoroughly , it means
The two women hate, each hates the other.
They cheated, one cheated another.
Here “each” and “one” belonged to the subject while “other” and “another” belong to the object. Therefore “each other” and one another are called as reciprocalpronouns and are rarely separated by even by a preposition.