what is the greatest common factor of $42a^5b^3$, $35a^3b^4$, and $42ab^4$?

$7ab^3$
$6a^4b$
$42a^5b^4$
$77a^8b^7$

Question

what is the greatest common factor of $42a^5b^3$, $35a^3b^4$, and $42ab^4$?

$7ab^3$
$6a^4b$
$42a^5b^4$
$77a^8b^7$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor of Monomials" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor of Monomials", "Factoring Polynomials by GCF" ] } ## Find the greatest common factor of the numerical coefficients $$ \text{gcd}(42, 35, 42) = 7 $$ ## Find the lowest power of each variable present in all terms $$ \begin{aligned} &\text{For } a: \min(5, 3, 1) = 1 \implies a^1 = a \ &\text{For } b: \min(3, 4, 4) = 3 \implies b^3 \end{aligned} $$ ## Combine the numerical and variable factors $$ \text{GCF} = 7 \cdot a \cdot b^3 = 7ab^3 $$

(A) $7ab^3$

(B) $6a^4b$

(C) $42a^5b^4$

(D) $77a^8b^7$

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

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QUESTION IMAGE

Question

Explanation:

Find the greatest common factor of the numerical coefficients

Find the lowest power of each variable present in all terms

Combine the numerical and variable factors

Answer: