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

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

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

Answer

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)