Question

find the gcf (greatest common factor) of the following terms.

\\(\\{x^2y^2, 5x^2y, 25x^2y^2\\}\\)

Explanation:

Find the GCF of the numerical coefficients

Using the Greatest Common Factor knowledge point

$$ \text{Coefficients: } 1, 5, 25 \implies \text{GCF}(1, 5, 25) = 1 $$

Find the GCF of the variable x

Using the Factoring Monomials knowledge point

$$ \text{Powers of } x: x^2, x^2, x^2 \implies \text{GCF}(x^2, x^2, x^2) = x^2 $$

Find the GCF of the variable y

Using the Factoring Monomials knowledge point

$$ \text{Powers of } y: y^2, y^1, y^2 \implies \text{GCF}(y^2, y, y^2) = y^1 = y $$

Combine the common factors

Using the Greatest Common Factor knowledge point

$$ \text{GCF} = 1 \cdot x^2 \cdot y = x^2y $$

Answer:

Find the GCF (greatest common factor) of the following terms.

$$ \{x^2y^2, 5x^2y, 25x^2y^2\} $$

Answer: <blank>\(x^2y\)</blank>