Although this is a mistake that could easily go unrecognized in verbal communication, such is not the case in writing. It becomes apparent that "would of" doesn't quite look right. The puzzling thing is that this mistake has become so prevalent, that people who make it often become desensitized to noticing on the page. Here is an illustration that may help you recall the proper way to write it in the future:
Here is an example that I have seen written online: Incorrect: "If it was me in that situation, I would of jumped over the fence." Correct: "If it was me in that situation, I would've jumped over the fence."
I hope that you have found this helpful. Even if you don't make this mistake frequently, I encourage you to share this post in your social media. Remember that if more people had shared this information with others in the past, they "could of" prevented this mistake from propagating.