Garage (ciment floor and paint)

I bought a 10 year old house 2 1/2 years ago.
The paint on the garage ciment floor is just about completely worned out.
Any recommendations on how to apply to paint:
-Do I have to strip the old paint?
-Do I have to sand away the old paint?
-Any kind of special preparation for the floor?
-Any recommended brand of paint?
-Any other recommendations so that I do not fall into beginners mistake?
Thanks

Sweep and clean very well. Then just paint on new cement paint. Lots of brands in lots of colors. Buy a wide paint brush and have fun.

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Jack the Contractor