The Common Core 6th Grade Math standards do not address prime factorization; however, I realize it is a strategy for finding GCF and LCM which are standards. In the GA Performance Standards, students were required to express numbers in prime factorization. Is this not the same for Common Core? I want to make sure that Common Core is not suggesting that students only list factors and multiples in order to find GCFs and LCMs. Thank you.
Greatest common factors and least common multiplies are treated with a very light touch in the standards. They are not a major topic, and limited to numbers less than or equal to 100 (6.NS.4). For such numbers, listing the factors or multiplies is probably the most efficient method, and has the added benefit of reinforcing number facts. It also supports the meaning of the terms: you can see directly that you are finding the greatest common factor or the least common multiple. The prime factorization method can be a bit mysterious in this regard. And, as you point out, prime factorization is not a topic in the Common Core, although prime numbers are mentioned in 4.OA.4. So, the standards do indeed remove this topic from the curriculum. Achieving the focus of the standards means giving some things up, and this is one of those things. (Of course personally, as a number theorist, I love the topic!)