QuestionAugust 24, 2025

Find the greatest common factor of 6xy^2 and 14y^3 6y^2 2xy^2 2 2y^2

Find the greatest common factor of 6xy^2 and 14y^3 6y^2 2xy^2 2 2y^2
Find the greatest common factor of 6xy^2 and 14y^3 6y^2 2xy^2 2 2y^2

Solution
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Answer

2y^{2} Explanation 1. Identify the factors of each term The expression 6xy^2 can be factored into prime numbers and variables as 2 \cdot 3 \cdot x \cdot y^2. Similarly, 14y^3 can be factored as 2 \cdot 7 \cdot y^3. 2. Determine common factors Identify the common factors between 6xy^2 and 14y^3. Both expressions have a common factor of 2 in terms of numbers. In terms of variables, they both have at least y^2. 3. Calculate the greatest common factor (GCF) Combine the common factors identified: 2 and y^2. Therefore, the GCF is 2y^2.

Explanation

1. Identify the factors of each term<br /> The expression $6xy^2$ can be factored into prime numbers and variables as $2 \cdot 3 \cdot x \cdot y^2$. Similarly, $14y^3$ can be factored as $2 \cdot 7 \cdot y^3$.<br />2. Determine common factors<br /> Identify the common factors between $6xy^2$ and $14y^3$. Both expressions have a common factor of $2$ in terms of numbers. In terms of variables, they both have at least $y^2$.<br />3. Calculate the greatest common factor (GCF)<br /> Combine the common factors identified: $2$ and $y^2$. Therefore, the GCF is $2y^2$.
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