Download Android APK files from the Google Play Store to PC

1) Assuming you are using the Chrome Browser on your desktop, download and install APK Downloader from the Chrome Web Store.

2) Once added to Chrome, just open any app page in Google Play and you will now see a Download APK option right next to install.

3) Click on it, and a popup will appear asking you for additional information. You will need your email address and the device ID of your phone.

4) For the Device ID, you can download the Device ID app from the Play Store or you can enter *#*#8255#*#* on your device’s Phone App (no need to press send) and look for a bunch of numbers and letters after either JID, Device ID, or aid. Mine was after aid and was at the top. Honestly, just download the Device ID app, it’s the easiest way.

5) You now need to enter your Gmail address that you use for your Play Store account. You will also have to enter your password. I know this might seem scary to some of you, but the information isn’t stored. Even though you won’t always be downloading paid apps, it’s the only way to ensure that no one is able to download something they didn’t pay for. Another reason is that Google tracks downloads for each app by Gmail address.

6) After you have entered all your information, click on Login, and close the window. You are now good to go, and you won’t have to enter your information again. Now when you click on Download APK, it will immediately be downloaded to your desktop. This will work for every app in Google Play, but if it’s a paid app, you won’t be able to unless you have previously purchased it using the Gmail account you logged in with.

Source: http://codekiem.com/2014/08/07/official-apk-downloader-v2-download-apk-files-from-google-play-store-to-pc/