Restoring Granite Tile Hearth

Hello All, I have recently purchased a 1927 Tudor in WA and am trying to restore the home. The fireplace has what appears to be original granite tile (5X5) (at least I think it's granite) for the hearth that has a few small chips, but is generally in good condition, except for the granite is completely dull and dingy. I've tried a few cleaning products, but the tile still looks old and grungy. I don't want to replace the hearth and think the granite would look great, but it definitely needs to be cleaned with something stronger than I'm using or needs to be polished somehow. Any suggestions out there? Thanks, David
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