The more easy way its by executing the next command:

ls -ls /usr/bin/python*

Output look like this:

/usr/bin/python           /usr/bin/python2.7        /usr/bin/pythonw
/usr/bin/python-config    /usr/bin/python2.7-config /usr/bin/pythonw2.7

It's normal to have many python binaries. You can see which is which in /usr/bin with this command:

$ ls -l /usr/bin/python*

You will see several links to different places. The native python is that one, which is in the /System/Library/Frameworks/Python.framework/Versions/2.7/bin/. Note that for OSX 10.9 (and for everything at least until 10.13) this is the python2, not python3. So you can safely remove all the other versions.

What are the other versions which you may have?

• Something downloaded from the official site python.org. It is located in /Library/Frameworks/Python.framework/Versions/. You can remove whatever in this folder you do not want. Removing the whole folder will completely remove Python including the original system version.
• Anaconda distribution is by default located in /Users/your_user/anaconda3/, but of course you may put in the other place. But if it contains anaconda in the path – it's Anaconda distribution. You may remove this folder.
• Either homebrew or port versions are in /opt/local/bin/. See the link destination with $ ls -l /opt/local/bin/python*. The best way of removing this is to use built-in commands like uninstall.
• Some packages might be in ~/Library/Python/ - that's from pip. You may safely remove the entire content of this folder in order to have a "clean" python.
• Finally, after you removed all the other versions, do not forget to remove the broken links to binaries, if there are still any.

See also this answer.

Homebrew installations are independent of macOS, you can neither update system components via Homebrew nor remove them with brew uninstall.

You could have multiple Python versions on your macOS.

You may check that by command, type or which command, like:

which -a python python2 python2.7 python3 python3.6

Or type python in Terminal and hit Tab few times for auto completion, which is equivalent to:

compgen -c python

By default python/pip commands points to the first binary found in PATH environment variable depending what's actually installed. So before installing Python packages with Homebrew, the default Python is installed in /usr/bin which is shipped with your macOS (e.g. Python 2.7.10 on High Sierra). Any versions found in /usr/local (such as /usr/local/bin) are provided by external packages.

It is generally advised, that when working with multiple versions, for Python 2 you may use python2/pip2 command, respectively for Python 3 you can use python3/pip3, but it depends on your configuration which commands are available.

It is also worth to mention, that since release of Homebrew 1.5.0+ (on 19 January 2018), the python formula has been upgraded to Python 3.x and a python@2 formula will be added for installing Python 2.7. Before, python formula was pointing to Python 2.

For instance, if you've installed different version via Homebrew, try the following command:

brew list python python3

or:

brew list | grep ^python

it'll show you all Python files installed with the package.

Alternatively you may use apropos or locate python command to locate more Python related files.

To check any environment variables related to Python, run:

env | grep ^PYTHON

To address your issues:

• Error: No such keg: /usr/local/Cellar/python

  Means you don't have Python installed via Homebrew. However double check by specifying only one package at a time (like brew list python python2 python3).

• The locate database (/var/db/locate.database) does not exist.

  Follow the advice and run:

  sudo launchctl load -w /System/Library/LaunchDaemons/com.apple.locate.plist
  

  After the database is rebuild, you can use locate command.