First, let us examine the causes of concrete cracks. If you reside in area where there is heavy snowfall then combination of snow and de-icing salts will cause many problems. The car will bring this in when you arrive and park the car in the garage. The de-icer salts are corrosive and will erode the concrete causing decay, and rainwater can seep through the span Crete and leak into the basement. As a consequence the garage floor will have wet, mildew, ugly patch. This could get worse when the leaking water seeps under the concrete slab, and it freezes lifting the slab and disappearing in the thaw. Over three months or so it could a lot damage to the floor. You will have an uneven floor.
Over last ten years many garage floor coating products have been developed to deal with this. The ideal solution would be to fill in the cracks in garage slab. The inside of the crack will be wet, wetness is due to moisture in the air, and the only thing that is going to work is Polyurea. Polyurea is strong enough to seal any wet areas. It needs to be soft enough with the right amount of fluid to spread into the crack and fill the gaps. Make sure when you are buying a filler that it is the right type because you do not one that will remain wet inside the crack. Applying a coating solution would be ideal, but very few work. The garage slabs have to properly clean and a costly epoxy resin applied over it, however you do run the risk of delamination. The floor may develop chipping and delaminating if the concrete garage paint is a cheap.
There are Polyurea and Polya spartic crack fillers available to deal with the most severe of weather conditions. The proper way is to grind the concrete garage surface, clean it of all bond breakers. The grinding will make the surface rougher and the coating will stick to it more readily. The new pure bred coaters will adhere to the surface layer of the concrete and seal it when it dries. The garage floor coating becomes a part of the garage foundations, rather being stuck on the surface.