FreeMantle, the 'of' sounds exactly the same as a V sound in speech. 'Of' is pronounced 'uv'. There is no F sound in it.
(The word 'off' has an F sound).
'Of' makes no sense at all grammatically. It's not part of the complete unit - 'could of'. It's a mistake based on the fact that the contraction 've (the last two letters of 'have') sounds exactly like the word 'of'.
'Could have', 'would have' and 'should have' are modal verbs. They are units consisting of verb (could, etc) + past participle (of the verb have). They make sense together. They indicate that something was possible in the past, or they speculate if something was possible in the past.
In the case of 'could have', we can use it interchangeably with 'might have'.
You can divide the parts of a modal verb up:
- Could someone have forgotten to put the cheque in the post?
- How could she have thought that colour would look good on her?
The negatives can also be divided up:
- Could she not have thought of something better to say than that?
The contractions also indicate something that might have or might not have been possible:
- She could've done far better than that layabout.
- He couldn't have enjoyed the movie as he had left his glasses in the car and his hearing aid wasn't working.
Contractions can be both positive and negative, and as long as you understand they include the shortened participle 'have' ('ve) they are perfectly valid no matter how awkward they may sound to any particular individual. But using 'of' is never correct even if it sounds right. Grammar matters.
When you speak it's impossible to tell whether you have the word 'of' or the contraction ''ve' in mind, but you can't write what you think sounds better. One way of writing the phrase is correct and all other versions are simply wrong.