To what extent did the Three Witches' prophecies lead to the downfall of Macbeth ?
This is an interesting question. The three witches seem to be predicting the future which is inevitable and unavoidable. It would seem that Macbeth was destined to murder King Duncan and usurp the Scottish throne regardless of what they told him, just as it was inevitable that Banquo's heirs would become kings of Scotland. Macbeth was encouraged to proceed with his plans by the witches' ambiguous prophecies, but he was already planning to murder Duncan before he and Banquo encountered the witches for the first time. This is shown in the opening of the fifth scene of Act 1 in which Lady Macbeth is reading her husband's letter aloud. Macbeth could not have avoided his fate. He could not have changed the future. This, of course, is a fatalistic view. There are scientists who claim that everything that has happened since the Big Bang and everything that will happen in the future was all predetermined because the Big Bang was the first cause which started an unbreakable chain of cause and effect. Very interesting question.
You could say that the witches were the catalyst. We will never know if Macbeth's greedy ambition lay in wait somewhere dark and dusty deep within his soul. We do know, however, that when he heard the witches' prophecy that he will someday be king, his thoughts immediately turn towards killing King Duncan. So, in a sense, it was not until he heard the witches that he gave credence to his own thoughts or ideas. After killing King Duncan he goes again to the three witches to seek guidance. Their prophecies are as follows: beware Macduff, no man of woman born can harm him, and until Birnam Wood marches up to Dunsinane (Macbeth's castle) Macbeth could not be conquered. Macbeth took these prophecies to heart, and in the end all three prophecies caused his ruin. Macbeth clutches at these prophesies until he sees Birnam wood begin to move up the hill towards his castle. He is then challenged by Macduff who is seeking revenge upon Macbeth for the slaughtering of is entire family and declares minutes before skewering Macbeth that he was ripped from his mother's womb and not born "naturally". So, overall, the witches' prophecies do bring about the ruin and downfall of Macbeth; without them, Macbeth probably would never had had the courage to do what he did.