Problem

7. Determine the greatest common factor of $12 x^{6} y, 4 x^{4} y^{2}$ and $6 x^{3} y^{4}$.

Answer

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Answer

\(\boxed{2x^3y}\) is the greatest common factor of the given expressions.

Steps

Step 1 ：Find the GCF of the coefficients: \(\text{GCF}(12, 4, 6) = 2\)

Step 2 ：Find the GCF of the powers of x: \(\text{GCF}(6, 4, 3) = 3\)

Step 3 ：Find the GCF of the powers of y: \(\text{GCF}(1, 2, 4) = 1\)

Step 4 ：Combine the GCFs of the coefficients and variables: \(2x^3y\)

Step 5 ：\(\boxed{2x^3y}\) is the greatest common factor of the given expressions.

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