1Cademy - Finding the GCF of $$4x^2y$$ and $$6xy^3$$

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Prime Factorization

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Finding the GCF of $4x^2y$ and $6xy^3$

To find the GCF of $4x^2y$ and $6xy^3$ , factor each expression completely and identify the shared factors.

Step 1 — Factor coefficients and expand variables: Write $4x^2y = 2 \cdot 2 \cdot x \cdot x \cdot y$ and $6xy^3 = 2 \cdot 3 \cdot x \cdot y \cdot y \cdot y$ .

Step 2 — Align factors in columns and circle the common ones: The shared factors are one $2$ , one $x$ , and one $y$ .

Step 3 — Bring down the common factors: Collect $2 \cdot x \cdot y$ .

Step 4 — Multiply: $2 \cdot x \cdot y = 2xy$ .

The GCF of $4x^2y$ and $6xy^3$ is $2xy$ . When expressions contain multiple variables, each variable is handled independently — the GCF includes each common variable raised to the lowest power found across all expressions.

Updated 2026-04-21

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OpenStax Elementary Algebra

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