Why is there 360' in a circle?

I have a basic understanding of radians, makes perfect sense to me.

But, why the value of 360 for the number of degrees in a circle?

Is there some specific mathematical reason, or is it just about convention and the vagueries of history?

I think it would make more sense to set 360', or 2 Pi radians, to a value of 1. Then successive divisions of an angle could be expressed in basic decimal form, i.e. 90'=0.25, 1/5 Pi radians=0.1 etc...