You can't make the crack go away as though it had never been there. Basically, you have three options:
1. If it's a clean break, you may be able to mend it if you remove both halves of the cracked piece from the floor, find the right glue/cement/epoxy, and tightly clamp the halves together while the adhesive sets. However, the mend won't last forever, and the crack will still be visible.
2. Accept that you have a crack, and fill it in with some kind of durable, long-lasting cement product, then seal the filler once it's set. You maybe be able to tint the cement so it looks more like part of the stone.
3. Remove the cracked piece of stone and have a replacement piece cut to match its dimensions. When you set it into the hole, try to make the cement match the original installation.
T. Nielsen Hayden, August 2009
