CF-Auto-Root is the best,the easiest and the safest way to root the Samsung Galaxy S4. Why is this the safest way? It roots the Galaxy S4 by installing SuperSU binary and SuperSU application.
Not a bad idea if you just want to root Galaxy S4. Plus you still can get OTA software update with stock recovery. Currently, it supports GT-I9505 Qualcomm LTE model only.The GT-I9500 is not supported but it will soon come for that version from the developer Chainfire.
How to know which Galaxy S4 model that you have? Go to Settings – More – About device – Model number. If it shows GT-I9505 you can download CF-Auto-Root. Don’t install on non-supported model. You will soft brick your Galaxy S4. And be sure to get more information at XDA website.
Download CF-Root for Samsung Galaxy S4 here.