Now ye are clean - Still keeping up the figure καθαροί katharoi. It does not mean that they were perfect, but that they had been under a process of purifying by his instructions all the time he had been with them. He had removed their erroneous notions of the Messiah; he had gradually reclaimed them from their fond and foolish views respecting earthly honors; he had taught them to be willing to forsake all things; and he had so trained and disciplined them that immediately after his death they would be ready to go and bear fruit among all nations to the honor of his name. In addition to this, Judas had been removed from their number, and they were now all true followers of the Saviour. See the notes at John 13:10.
Through the word - By means of the teachings of Jesus while he had been with them.