Can you solve the "Census Taker and Mathematician" puzzle?

A census taker phones a household to obtain information about the ages of the children residing there. Unfortunately for the census taker, the father is a mathematician who gives her only the following the clue:

"I have three children. The product of their ages is 72 and the sum of their ages is the number of my house."

The census taker (who knows the number of the house) struggles for a while and complains that she hasn't been given enough information. The father replies:

"I forgot to mention that my oldest child loves chocolate chip cookies."

The census taker is then able to work out the children's ages.

What are the children's ages?

Here's the solution, with a full explanation ...

Didn't figure it out after about 3 minutes of trying.

You (or the problem) should have given us the number of the house if the census taker knew it.

I got up as far as figuring out the possibilities:

72 1 1

36 1 2

18 2 2

12 3 2

9 4 2

6 6 2

24 1 3

12 2 3

8 3 3

6 4 3

18 1 4

9 2 4

12 1 6

9 1 8

These are all the possible sets of 3 numbers that all have the product of 72. Repeated numbers in one set implies twins.

-Byshop

I figured it out in around 20 seconds.

We did plenty of similar problems in introductory maths class.

Since I can't get to Youtube at work, the video is worthless. Without the number of the house, this problem isn't solvable and I fail to see how the child's love of chocholate chip cookies adds anything.

If someone that was able to view the Youtube video can explain, I would be appreciative.

What it means is oldest child, not oldest children. Which is to say, something like 2, 6, 6 is ruled out

Correct. The key to the puzzle is that the census taker couldn't work out the ages with the house number alone, but could work them out with the house number and the knowledge that there is a single oldest child.

So just enumerate all the ways 72 can be broken into 3 factors. For each factoring, find the sum of the factors. Then look for a group of factorings that share the same sum, but where only one of the factorings has an oldest child. That latter factoring is the answer.

@Byshop: that is the correct answer. EAT THE LIVER!