Question

what is the greatest common factor of $42a^{5}b^{3}$, $35a^{3}b^{4}$, and $42ab^{4}$?
$6a^{4}b$
$42a^{5}b^{4}$
$77a^{8}b^{7}$
$7ab^{3}$

Explanation:

Step1: Find GCF of coefficients

Factor each coefficient:
$42 = 2 \times 3 \times 7$, $35 = 5 \times 7$, $42 = 2 \times 3 \times 7$
The common prime factor is 7, so GCF of coefficients is 7.

Step2: Find GCF of $a$-terms

For $a^5$, $a^3$, $a^1$, take the lowest exponent: $a^1 = a$

Step3: Find GCF of $b$-terms

For $b^3$, $b^4$, $b^4$, take the lowest exponent: $b^3$

Step4: Multiply all GCF parts

Multiply the results from steps 1-3: $7 \times a \times b^3$

Answer:

$7ab^3$