Question

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

Explanation:

Step1: Find GCF of coefficients

Find GCF of 60, 45, 75.
Prime factors:
$60=2^2\times3\times5$, $45=3^2\times5$, $75=3\times5^2$
GCF = $3\times5=15$

Step2: Find GCF of $x$-terms

Find lowest power of $x$: $x^4, x^5, x^3$.
Lowest exponent is 3, so GCF is $x^3$

Step3: Find GCF of $y$-terms

Find lowest power of $y$: $y^7, y^5, y^1$.
Lowest exponent is 1, so GCF is $y$

Step4: Combine all GCFs

Multiply the GCFs from steps 1-3.
$15\times x^3\times y = 15x^3y$

Answer:

15$x^3y$