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What equipment have you been using to clean it?
Most of the floor has been down for over 5 years. Had some tiles replaced these tiles have what looks like cement residue over them as detailed in the photo. They have been down for about one year.Is this a new floor, as you say grout deposits on the tiles.
You ideally need a rotary with soft to medium brush and a wet vac then I would use then since you are already using LTP grout stain remover pre-wet the floor put it on agitate it and allow to dwell 5-10minutes then agitate again then vac it up. Allow it to dry personally give it a good 24hours so the stone is dry surface and throughout the whole stone then seal with a colour enhancing sealer.
Sorry just to clarify i should use some LTp grout stain remover and agitate with a brush, before resealing.