A wizard has 3 children.He meets a warlock who wants to know the ages of the 3 children.Ages are whole numbers

Question

The product of their ages is 72 and the sum of their ages is the witches he said he had seen on the way to work that morning.
The warlock needed more information.
The wizard tells him his youngest child is named Harry.
The warlock knows the ages now.

The ages are 6,6 and 2. But why?
This involves logic, such as when he talks about Harry, it means he has a youngest child ie he does not have 2 children with the same age being youngest

Answer 1

The answer is 6,6 and 2.
The reason is that 6,6 and 2 are the only three factors of 72 multiplied together, two of which are the same number.
The clue is that when the wizard told the warlock that the youngest was called Harry, the warlock then knew the answer.
How did he know? - Because he could see that the older two were twins. Therefore, 6,6 and 2 is the answer
Edit:
The number of witches is unnecessary information, and a red herring. I also liked your question in its earlier form.
Further edit; You need to know Harry is youngest, because 3,3,and 8 works also.
A Very good question!

Answer 2

there are 2 sets of 3s that are factors of 72,
72=2.6.6=3.3.8
which at the same time have the same sum, 14(also the no of witch wizard passed by).

since the sum(14) itself cant give a clear answer to the warlock, he had to ask for another clue.

from "youngest" clue, its clear the ans =2,6,6

Answer 3

to be honest with you there is no way to tell the exact ages of all three children from this information you needed to be told that he had twins.
yes if you factor 72 you get 6,6,2 but you can further factor the 6's so that you get: 3,3,2,2,2,1 so they could be any combination. so you would either had to know he had twins or one of there ages.