Pudding Survey

A man is doing a pudding survey. He needs to know the ages of kids that like pudding. He knocks on one house's door. A woman answers. The man asks, "...If you have any kids, what are their ages and do they like pudding?" The woman responds, "I have three kids. The product of their ages is 72 and the sum of their ages is my house number." The man looks at the house number. Being a statistician, he is no stranger to math and gets to calculating. He responds with, "Ma'am, I still don't know the ages of your kids." The woman says, "Oh! My oldest child likes pudding." The man instantly writes down the ages of the kids and which of them like pudding and continues on to the next house. How old are the children?