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

The coefficients are 60, 45, 75. Prime factorize:
\(60 = 2^2 \times 3 \times 5\), \(45 = 3^2 \times 5\), \(75 = 3 \times 5^2\).
Common factors: \(3 \times 5 = 15\).

Step2: Find GCF of \(x\)-terms

For \(x^4\), \(x^5\), \(x^3\), the smallest exponent is 3. So \(x^3\).

Step3: Find GCF of \(y\)-terms

For \(y^7\), \(y^5\), \(y\), the smallest exponent is 1. So \(y\).

Step4: Combine results

Multiply the GCF of coefficients, \(x\)-terms, and \(y\)-terms: \(15 \times x^3 \times y = 15x^3y\).

Answer:

B. \(15x^3y\)