Brain Teaser: Can You Guess A Kid’s Age Based On Their Red Hair?

It’s that time again: prepare your brain for some hard-core teasing.
Yep, we heard you. The last puzzle we shared was way too easy.
You won't feel that way about our latest.
This week’s head-scratcher comes from i09 and involves some pretty savvy thinking.
Here’s one thing to remember: it may sound totally abstract, but the final clue really does hold the answer to solving this curious tangle.
Ooh, you're intrigued now! Read the following very carefully and see how quickly the answer comes to you.
Two former college roommates, both logicians, meet at a conference after many years without contact. While catching up, the two eventually get around to discussing their children. The first logician asks the second how many children he has, and what their ages are. The second replies that he has 3 children, but (ever the logician) he will only reveal clues about their ages. The first logician must deduce for himself the ages of the second's children.
"First," says the logician, "the product of my children's ages is 36."
"Second, the sum of their ages is the same as our apartment number in college."
"Third, my oldest child has red hair."
Upon hearing the third clue, the first logician replies at once with the ages of his friend's children.
1) What are they? 2) How do you know?
Check back tomorrow for the answer, brainiacs! Show your working in the comments section below.
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