Senegoid, does the textbook say that it’s designed for the Common Core? Why do you assume that it is? As Amateur Barbarian pointed out, let’s make sure the examples we’re discussing are actually from the Common Core before we blame them on it.

The problems with the question in the OP certainly predate the Common Core. Richard Feynman in one of his books gave an example from a 1964 arithmetic book in California which sounds rather similar. There was a question in the book that went something like this (although I’m reconstructing from memory and the details are definitely not correct): Stars of different colors have different temperatures. Red ones have temperatures of 4000 degrees, yellow ones of 5000 degrees, blue ones of 6000 degrees, and green ones of 7000 degrees. If you put together two red stars, one yellow one, three blue ones, and five green ones, what temperature will the result be?

Now, even if those temperatures are correct, you can’t add together temperatures and have them say anything about the temperature of the resulting thing, so this is simply a bad example of whatever they’re trying to teach. So why was such a question written? It was because the textbook writers were told that they had to come up with word problem questions for every idea they introduced. Coming up with word problems isn’t that bad in itself. A lot of students will learn the mathematical techniques that solve problems, but they can’t translate them into real life at all. Word problems can be useful in teaching them to translate back and forth from words to equations. Furthermore, the textbook writers were told that it would be nice if the word problems relied on material from science. So the textbook writers started flipping through books or articles about astronomy. They found mentions of the different temperatures of different colors of stars, so they threw that into the question, despite the fact that they didn’t remotely understand the notion of combining temperatures. The problem is that textbook writers are often hacks who will do whatever the textbook publishers and the state textbook committees tell them, even though the writers don’t understand what they’re doing.

The same thing happened in the question in the OP. The writers were told to teach the idea of the factors of a number and to make up word problems about it so that they could be sure that the students understood the concept and could translate back and forth from equations to words. The writers found somewhere a mention of snowflakes. They decided to use snowflakes as an example. They need to have several different kinds of snowflakes. Maybe or maybe not there are various shapes of snowflakes, but they decided that there are. So the word problem says that a total of 36 snowflakes were made. The problem says that the total number of snowflakes is a multiple of the number of triangular snowflakes. The student is supposed to be able to see that 36 is a multiple of (i.e., has factors of) 1, 2, 3, 4, 6, 9, 12, and 18. (Well, and maybe 36, if your definition says that a number is a multiple of itself or is a factor of itself.)

The problems predate the Common Core by a long time. The problem is that the textbooks are written by hacks who are trying to slavishly follow the instructions of publishers and textbook committees and the organizations who lobby the committees. Everybody has an agenda, often a political one of the right or the left, and no one is really trying to create a great textbook. Everyone is trying to avoid getting fired from their jobs, so they follow instructions no matter what. Their job isn’t producing a great textbook; rather, it’s following the instructions they’re given.