what is the greatest common factor of 42a^5b^3, 35a^3b^4, and 42ab^4?\n7ab^3\n6a^4b\n42a^5b^4\n77a^8b^7

Explanation:

Step1: Find GCF of coefficients

Find GCF of 42, 35, 42. Prime - factorize: 42 = 2×3×7, 35 = 5×7, so GCF(42,35,42)=7.

Step2: Find GCF of a - terms

For $a^5$, $a^3$, $a$, the lowest power of a is $a^1$ (since $a=a^1$).

Step3: Find GCF of b - terms

For $b^3$, $b^4$, $b^4$, the lowest power of b is $b^3$.

Step4: Combine GCFs

The GCF of the three terms is the product of the GCF of coefficients and GCF of variables, which is $7\times a\times b^3 = 7ab^3$.

Answer:

A. $7ab^3$