find the greatest common factor of these two expressions.

(16y^6 u^2) and (12v^5 y^7 u^4)

Question

find the greatest common factor of these two expressions.

(16y^6 u^2) and (12v^5 y^7 u^4)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Greatest Common Factor", "Algebraic Expressions" ], "current_concepts": [ "Greatest Common Factor", "Algebraic Expressions" ] } ## Find the greatest common factor of the numerical coefficients $$ \gcd(16, 12) = 4 $$ ## Find the greatest common factor of the variable parts $$ \begin{aligned} &\gcd(y^6, y^7) = y^{\min(6, 7)} = y^6 \ &\gcd(u^2, u^4) = u^{\min(2, 4)} = u^2 \ &\gcd(1, v^5) = 1 \end{aligned} $$ ## Combine the numerical and variable factors $$ \text{GCF} = 4y^6u^2 $$ $4y^6u^2$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Greatest Common Factor" ] }

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QUESTION IMAGE

Question

Explanation:

Find the greatest common factor of the numerical coefficients

Find the greatest common factor of the variable parts

Combine the numerical and variable factors

Answer: