Would You Treat A Census-man This Way?

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A census-taker knocks on a door, and asks the woman inside how many children she has and how old they are.

"I have three daughters, their ages are whole numbers, and the product of the ages is \(36\)," says the mother.
"That's not enough information," responds the census-taker.
"I'd tell you the sum of their ages, but you'd still be stumped."
"I wish you'd tell me something more."
"Okay, my oldest daughter Annie likes dogs."

What is the age of the eldest daughter?

\(\text{This problem is not original.}\)


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