Two well-known logicians, Alfred and Bilber, meet at a conference. Following conversations takes place between them.
Alfred: I have three daughters. Product of their completed ages is 360.
Bilber: I can’t figure out the exact ages of your daughters. I need one more hint.
Alfred: Sum of their ages is exactly half of my age.
Bilber: I know your exact age. But still I can’t tell. One more hint please.
Alfred: Average age of my daughters requires an addition of 1/3 to get an integer.
Bilber: This doesn’t provide me any additional information. Any other hint please.
Alfred: The age difference between oldest and middle daughter is more than 1, but less than 5.
Bilber: Now, I know their exact ages.

Can you tell the ages of three daughters (in completed years)?