How long does it take for babies umbilical cord stump to drop off?

A baby’s umbilical cord will gradually drop off within a week. In the meantime, keep it clean and dry at all times. Simply dampen a cotton wool or bud with cooled boiled water to clean the cord. Clean in an upwards motion from the base and changing to a new clean piece after each bath or when it is wet. Information taken from: http://www.kkh.com.sg/HealthPedia/Pages/PregnancyAfterGoingHome.aspx