Question

find the gcf for the following list.

• 20x²y, 4x²y³, 60x³y³

the gcf is \square. (simplify your answer.)

Explanation:

Step1: Find GCF of coefficients

Find the greatest common factor of 20, 4, 60.
Factors of 20: 1,2,4,5,10,20
Factors of 4: 1,2,4
Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60
GCF of coefficients is 4.

Step2: Find GCF of $x$-terms

Identify the lowest power of $x$: $x^2$, $x^2$, $x^3$.
Lowest power is $x^2$.

Step3: Find GCF of $y$-terms

Identify the lowest power of $y$: $y^1$, $y^3$, $y^3$.
Lowest power is $y^1 = y$.

Step4: Combine all GCF parts

Multiply the GCF of coefficients, $x$-terms, and $y$-terms.
$\text{GCF} = 4 \times x^2 \times y$

Answer:

$4x^2y$