How can I remove sticky residue from uplifting carpet tiles stuck on a kitchen floor?

Previous homeowner stuck carpet tiles on to kitchen tiles. We removed them and although we cant see any sticky stuff I'm sure its not totally glue free as kitchen floor keeps hold of dirt and grime and always seems to be a bit grubby and a little sticky and dirty. I want a really clean kitchen floor. I've tried Jif and hot water, on my hands and knees! Any ideas please?