Fixing Ceramic Floor Tile

I just bought a new house (not a NEW house - it was built in 1966). There's a ceramic tile floor in the kitchen. One of the tiles is loose and there is grout missing from around the tile.
What's the best way to fix this? Should I try to pull the tile out and reset it or can I just grout around the tile? Will that secure the tile?
What should I use to do this? Thanks.
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Go to the hardware store for pre-mixed tile repair grout. It is way more expensive than powdered grout, but for just a few tiles it is the cost effective way to go. Remove the whole tile if it will come up without breaking and slobber the pre-mix all under and around it.

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Jag,
I had about 7 loose tiles in my foyer (9"sq). I cut as much grout out with a 4-1/2" diamond saw blade on an angle grinder (very dusty). DeWalt sells the blade for about $11 U.S. I then started picking up tiles. I think I lost 2 to breakage. Cleaned up area under tiles down to underlayment, and removed any loose grout. I used notched trowel to apply new thinset (one with latex additives). Let tiles set about 48 hours, and grouted.
-- Best Regards, Dennis J Sunday Home Inspection Systems Www.homeinspectionsystems.com

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JAG writes:

The tile needs suppport fully underneath or it will crack under a load. You must pull it up. You must chip and scrape most of the old thinset off both tile and floor. You must use a notched trowel to spread new thinset in ridges over the entire tile or bare floor. The ridges are critical to give room to squish the tile back to the original level. Grout after that sets. Shortcuts will leave the tile off level or cracked under load.
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Before you do this, can you match the existing grout? If yes, take out the remaining grout. Determine how loose the tile is to determine how much force is needed to get the tile out. Careful, as you don't want to crack the tile. Perhaps you could look around the basement and/or garage to see if the previous owner left any spare tiles around. I might start with a broad bladed putty knife and move up to a prybar of some small sort. The tile should come up pretty easily. Be careful not to try to lift up any mortar bed that may be there.
Once the tile is up, pick up some premixed mortar (usually a thinset--check with the local home depot or similar). Plop the tile back on, smoosh it around. Level to surrounding tile. Be careful to properly space the tile to line it up with existing tiles. Clean up any excess cement in the tile space. Let dry. Grout.

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