what is the greatest common factor of (4xy^2) and (20x^2y^4)?

* (24xy^2)
* (4xy^2)
* (24xy)
* (4xy)

Question

what is the greatest common factor of (4xy^2) and (20x^2y^4)?

* (24xy^2)
* (4xy^2)
* (24xy)
* (4xy)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor Factoring" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor Factoring" ] } ## Find the greatest common factor of the numerical coefficients Using the *Greatest Common Factor Factoring* knowledge point $$ \text{GCF}(4, 20) = 4 $$ ## Find the greatest common factor of the variable parts Using the *Greatest Common Factor Factoring* knowledge point $$ \begin{aligned} &\text{GCF}(x, x^2) = x^{\min(1, 2)} = x\ &\text{GCF}(y^2, y^4) = y^{\min(2, 4)} = y^2 \end{aligned} $$ ## Combine the numerical and variable factors Using the *Greatest Common Factor Factoring* knowledge point $$ \text{GCF}(4xy^2, 20x^2y^4) = 4 \cdot x \cdot y^2 = 4xy^2 $$

(A) $24xy^2$

(B) $4xy^2$

(C) $24xy$

(D) $4xy$

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

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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: