use prime factorizations to find the gcf of 18 and 33.
prime factorization of 18: $2 \times 3 \times 3$
prime factorization of 33: $3 \times 11$
the gcf of 18 and 33 is

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Prime Factorization", "Greatest Common Factor" ], "new_concepts": [], "current_concepts": [ "Prime Factorization", "Greatest Common Factor" ] } ## Identify the prime factorizations $$ \begin{aligned} 18 &= 2 \times 3 \times 3 \ 33 &= 3 \times 11 \end{aligned} $$ ## Find the common prime factors $$ \text{Common factors} = \{3\} $$ ## Calculate the GCF $$ \text{GCF} = 3 $$ Use prime factorizations to find the GCF of 18 and 33. Prime factorization of 18: $2 \times 3 \times 3$ Prime factorization of 33: $3 \times 11$ The GCF of 18 and 33 is 3. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Greatest Common Factor" ] }

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Question

Explanation:

Identify the prime factorizations

Find the common prime factors

Calculate the GCF

Answer: