Can we install Android 4.4 factory image on Samsung Galaxy Core? Google has released Android 4.4 factory image for Nexus 4 and Nexus 7 today. The steps to install Android 4.4 factory image in nexus 4 is


Download the factory image corresponding to your device's model and version
Extract the downloaded file and cd into the extracted directory.
run adb reboot-bootloader
run ./flash-all.sh


Can I follow the same steps and install the above Android 4.4 in Samsung Galaxy Core or in Galaxy Grand? Any help will be highly appreciated?
No, you can't. Those ROMs are intended for those devices only. Flashing a ROM that is not compatible with the device can brick the device.

You should wait for 4.4 ROMs for your devices.