identify the greatest common factor of $45a^3w^3$ and $18a^5w^4$.

a $18a^3w^4$

b $45a^3w^3$

c $9a^3w^4$

d $9a^3w^3$

Question

identify the greatest common factor of $45a^3w^3$ and $18a^5w^4$.

a $18a^3w^4$

b $45a^3w^3$

c $9a^3w^4$

d $9a^3w^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules" ], "new_concepts": [ "Greatest Common Factor", "Monomial Factoring" ], "current_concepts": [ "Greatest Common Factor", "Exponent Rules", "Monomial Factoring" ] } ## Encontrar el máximo común divisor de los coeficientes numéricos $$ \text{mcd}(45, 18) = 9 $$ ## Encontrar el menor exponente para cada variable común Using the **Exponent Rules** knowledge point: $$ \begin{aligned} &\text{Para } a: \min(3, 2) = 2 \implies a^2 \ &\text{Para } w: \min(3, 4) = 3 \implies w^3 \end{aligned} $$ ## Combinar los factores para obtener el máximo común divisor $$ \text{MCD} = 9a^2w^3 $$

(A) $18a^2w^4$

(B) $45a^3w^3$

(C) $9a^3w^4$

(D) $9a^2w^3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Greatest Common Factor" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Encontrar el máximo común divisor de los coeficientes numéricos

Encontrar el menor exponente para cada variable común

Combinar los factores para obtener el máximo común divisor

Answer: