Samsung might not be a developer community favorite, but gaining root access on its devices has been particularly easy. However, with the Galaxy S4 things are a bit different this time. Gaining root access on the Exynos 5 Octa variant of the Galaxy S4 (I9500) has proven particularly tricky for developers. On the other hand, rooting the Qualcomm (I9505) variant is pretty straight forward and involves the use of ODIN.

Luckily, since the Exynos 5 Octa variant is being sold only in limited non-LTE markets, so chances are you must be owning the Qualcomm (I9505) variant of the Galaxy S4. So, if you are looking to gain root access on your SGS4, here is how you can do so in five simple steps -:

Keep in mind that the steps below are only for the I9505 or the Qualcomm variant of the Galaxy S4. Do not play around with the settings in ODIN. Let everything remain as it is.

1. Download ODIN, CF-Auto Root from Chainfire and the required drivers. Install the drivers, and extract the contents of the CF-Auto Root zip file inside a new folder on your desktop. The file you will extract from the zip file will have a .tar extension. Do not extract the contents of the tar file.
2. Fire up ODIN, and click on the PDA button. Then navigate to the new folder on your desktop that contains the tar file that you extracted from the CF-Auto Root zip file in Step 1.  
3. Switch off your Galaxy S4. Now, you need to put it in ‘Download’ mode by pressing the Volume Down + Home + Power button simultaneously. You will get a warning saying that using a custom OS will harm your device etc., which you can skip by pressing the Volume up button. 
4. Connect your S4 to your PC now. Once the drivers are automatically installed, ODIN will detect your phone and display a random COM No. Click on the ‘Start’ button and now wait for ODIN to flash CF-Auto-Root. The whole procedure should not take more than 30 seconds.
5. Once the flashing procedure is completed, your phone will automatically reboot.

You have now successfully managed to gain root access on your Galaxy S4. Keep in mind that CF-Auto-Root does not install a custom recovery, so you cannot flash any custom kernel or any mods. Installing a custom recovery is very easy, and you just need to use ROM Manager or the Goo.im app to install either CWM or TWRP recovery on your Galaxy S4.

Thanks to Chainfire for all his hard work!