My Phone keeps Turning off for no reason.

My galaxy s4 (GT-i9505 keeps shutting down<br> for no reason as if it doesn't have any battery<br> left. It was rooted and I had downloaded a lot<br> for 3rd part apps. At first I though that was the<br> problem, but I wasn't. I unrooted my device,<br> factory reset it and cleared all cash. I don't<br> know what the problem is.<br> Could it be that my battery is broken? But I<br> only have had the phone for a couple of Months.<br> Every time it shutdown there is a gap in the<br> amount of battery left. When it shutdown and I<br> plug it into the charger it shows as if there is no<br> battery left and then after a couple of seconds<br> show that amount of battery there was before<br> shutdown.<br> Right before this started happening I have<br> noticed my phone was heating up even when<br> not doing anything.