Question

find the gcf for the following list
-42x²y², 21x³y³, 84x⁴y³
the gcf is
(simplify your answer)

Explanation:

Step1: Find GCF of coefficients

Find the greatest common factor of -42, 21, 84.
Factors of 42: $1, 2, 3, 6, 7, 14, 21, 42$
Factors of 21: $1, 3, 7, 21$
Factors of 84: $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$
The GCF is $21$.

Step2: Find GCF of $x$-terms

Find the lowest power of $x$ among $x^2, x^3, x^4$.
The lowest exponent is 2, so GCF is $x^2$.

Step3: Find GCF of $y$-terms

Find the lowest power of $y$ among $y^2, y^3, y^3$.
The lowest exponent is 2, so GCF is $y^2$.

Step4: Combine all GCF parts

Multiply the GCF of coefficients, $x$-terms, and $y$-terms.
$21 \times x^2 \times y^2$

Answer:

$21x^2y^2$