Igor and Ivan are chatting on a plane. Igor asks, "What are the ages of your three sons?". Ivan responds, "The product of the ages of my three sons is 36, while the sum of their ages is today's date." Igor thinks for a while, only to respond, "I don't yet have enough information to deduce the ages of your three sons." To that, Ivan responds, "Ah yes. My oldest son has red hair." Igor says, satisfied, "Now, I know the exact ages of your sons."
Challenge: What are the ages of Ivan's sons, and how did Igor find out?