Question

what is the greatest common factor of $60x^{4}y^{7}$, $45x^{5}y^{5}$, and $75x^{3}y$?
$\bigcirc$ $5xy$
$\bigcirc$ $15x^{3}y$
$\bigcirc$ $45x^{3}y^{5}$
$\bigcirc$ $75x^{5}y^{7}$

Explanation:

Step1: Find GCF of coefficients

Factor each coefficient:
$60 = 2^2 \times 3 \times 5$
$45 = 3^2 \times 5$
$75 = 3 \times 5^2$
The common prime factors are $3$ and $5$, so GCF of coefficients is $3 \times 5 = 15$.

Step2: Find GCF of $x$-terms

For $x^4$, $x^5$, $x^3$: the lowest exponent of $x$ is $3$, so GCF is $x^3$.

Step3: Find GCF of $y$-terms

For $y^7$, $y^5$, $y^1$: the lowest exponent of $y$ is $1$, so GCF is $y$.

Step4: Combine all GCF parts

Multiply the GCF of coefficients, $x$-terms, and $y$-terms together.
$15 \times x^3 \times y = 15x^3y$

Answer:

B. $15x^3y$