Definition of each determiner from the Oxford Advanced American Dictionary

  

each

 determiner,pronoun
determiner, pronoun
NAmE//itʃ//
 
 
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 used to refer to every one of two or more people or things, when you are thinking about them separately Each answer is worth 20 points. Each of the answers is worth 20 points. The answers are worth 20 points each. “Red or blue?” “I'll take one of each, please.” We each have our own car. There aren't enough books for everyone to have one each. They lost $40 each. Each day that passed he grew more and more desperate.
Grammareach / everyEach is used in front of a singular noun and is followed by a singular verb:Each book is labeled with a price.It is usually preferable to use their instead of his or her, even in the singular:Each student will be given their own e-mail address.When each is used after a plural subject, it has a plural verb:They each have their own e-mail address.Every is always followed by a singular verb:Every student in the class is capable of passing the exam.Each of, each one of, and every one of are followed by a plural noun or pronoun, but the verb is singular:Each (one) of the houses was slightly different. I bought a dozen eggs and every one of them was bad.
See the Oxford Advanced Learner's Dictionary entry: each