The Census Taker’s Last Clue

A census taker knocks at a house and asks a parent for the ages of her three daughters. She replies, “Their ages are whole numbers, and if you multiply them together, you get thirty-six.” “That does not tell me enough,” says the census taker. “Their ages add up to the number displayed on the house directly across the street,” she adds. The census taker looks at the number opposite, thinks for a moment, and says, “I still cannot determine their ages.” The parent then says, “My eldest daughter plays the piano.” With that final remark, the census taker knows all three ages. How old are the daughters?