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For Geeks & Brainiacs #21- How Many Children -

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Puzzle Image A pizza delivery man named Mario (who also happens to be a mathematician) arrives at a house with a stack of pizzas and rings the doorbell. Mr. White, the owner of the house, opens the door. Mario hears several children inside playing together noisily. "Big family!" Mario says. "It's a birthday party. My children are playing with friends from three other families." Mr. White replies. "My wife and I have the most children, followed by the Browns, the Greens, then the Reds. Each family has a different number of children." Mr. White adds.

"How many children are in there?" Mario asks. "Fewer than 18 and the product of the number of children in each of the four families is the same as our house number." Mr. White answers with a grin. Mario looks at the house number and does some calculations on his notepad. "That's not enough information. Is there more than one child in the Red family?" Mario inquires. When Mr. White replies, Mario correctly states the number of children that are there. So how many children are there?
Do you have a suggestion for this puzzle (e.g. something that should be mentioned/clarified in the question or solution, bug, typo, etc.)?