what is the greatest common factor of $60x^{4}y^{7}$, $45x^{5}y^{5}$, and $75x^{3}y$?\n$5xy$\n$15x^{3}y$\n$45…
what is the greatest common factor of $60x^{4}y^{7}$, $45x^{5}y^{5}$, and $75x^{3}y$?\n$5xy$\n$15x^{3}y$\n$45x^{3}y^{5}$\n$75x^{5}y^{7}$
Answer
Explanation:
Step1: Find GCF of coefficients
Find GCF of 60, 45, 75. Prime - factorize: 60 = 2×2×3×5, 45 = 3×3×5, 75 = 3×5×5. GCF(60, 45, 75)=15.
Step2: Find GCF of x - terms
For (x^{4}), (x^{5}), (x^{3}), the lowest power of x is (x^{3}) (using the rule that for (x^{m}), (x^{n}), (x^{p}), GCF is (x^{\min(m,n,p)})).
Step3: Find GCF of y - terms
For (y^{7}), (y^{5}), (y), the lowest power of y is y (using the rule that for (y^{m}), (y^{n}), (y^{p}), GCF is (y^{\min(m,n,p)})).
Step4: Combine GCFs
The GCF of (60x^{4}y^{7}), (45x^{5}y^{5}), and (75x^{3}y) is the product of the GCF of coefficients and GCF of variables, which is (15x^{3}y).
Answer:
B. (15x^{3}y)