Google released Google Play Store 7.3.07.K-all  [PR] 139935798 few days ago out-dating all earlier versions. You can download this apk free from here. This version of the Play Store will run on devices running from Android 4.0 (Ice Cream Sandwich) to Android 7.1 Nougat.
Google Play Store 6.x.x APK Download Free
This post is to list the latest Google Play Store 6.x.x version and link for APK download. Play Store been getting updates regularly every now and then. Changed upgraded the design, experience and brought it to the next level. I guess, in the last few months Google has been doing some A/B Testing with the Play Store app for Android. Releasing different version numbered app in different time-frame. Now, there are few different versions of the app that supports different Android platform. Check your Android version and select the right Play Store APK for your device from below.
Google Play Store 4.1.10 Download and Install on Your Android
Google Play Store download is here. The Play Store got updated again. This time another incremental update brought the Google Play Store to 4.1.10 version. The previous version was released on 14th May evening and the version was 4.1.6 prior to Google I/O 2013. Even before than there was few more update and the UI change which we talked about here before.