Is it possible to do a factory reset without losing application data? I need to do factory reset of my phone, but don't want my applications to lose data.

Is it possible to somehow move the apps to SD card and, later, back to the phone?
A quick search provides:

~ Titanium Backup
~ Helium
~ (you guessed it) App Backup and Restore

http://www.androidheadlines.com/2015/02/featured-top-10-backup-apps-android.html

I've used and personally prefer Titanium