Why are there three witches in "Macbeth"?
'Witches' is ambiguous. Confusion has largely arisen because the Folio text refers to them in stage directions and speech prefixes as 'witches'. They call themselves the 'Weird Sisters' and Banquo and Macbeth refer to them as such. The only time the word 'witch' is actually heard in the theatre is in line 6 of I,iii when the First Witch quotes the words of the sailor's wife as the supreme insult for which her husband must be tortured.
'Weird' did not come into its modern usage before the 19th Century - it meant Destiny or Fate, and foreknowledge is clearly the Sisters' chief function. But their powers remain ambiguous - they are actively malicious to the 'master o' the Tyger' but don't have the power to destroy him. They appear to Macbeth at will - theirs and his - but confine their interference to prediction. These powers - to hex and predict - were attributed to village witches, but the Weird Sisters are more decisively supernatural, and the ambiguity (of nature, and of power) is fundamental to the ambiguities of experience and knowledge (does Banquo's ghost 'exist' for any but Macbeth, for instance? And what about the Dagger?) as the play develops.
The three witches in the book was used to represent the three Fates of the ancient mythology, who impersonally weave the threads of human destiny. They take in delight in their power of foretelling the future to play and toy with human's feelings and later destroy them.
The number 3 has, historically, always had a magical quality. The number appears many times throughout the play; 3 witches, 3 prophecies, 3 apparations, etc. The "temptation" scene is even the third scene of Act I, and the wiches tend to repeat the same thing, saying it "thrice". I really like Roman Polanski's version of Macbeth and his interpretation of the three witches; it is very druidic. There's 2 older ones and one younger one, almost like the "witch in training. ' He also presents one witch whose eyes are covered (or maybe aren't even there!), one with her ears covered and the third one does not speak...is it a suggestion of see no evil, hear no evil, speak no evil??? Interesting interpretation, nonetheless.