#### Answer

a) $5q^{2}$
b) 1

#### Work Step by Step

Factors of $15q^{3}$ : 3 $\times$ 5 $\times$ q $\times$ q $\times$ q
Factors of $40q^{2}$ : 2 $\times$ 2 $\times$ 2 $\times$ 5 $\times$ q $\times$ q
a) They both have a 5 $\times$ q $\times$ q common, thus the greatest common factor of is $5q^{2}$
Factors of $3q$ : 3 $\times$ 1 $\times$ q
Factors of 8: 1 $\times$ 2 $\times$ 2 $\times$ 2
b) They both have a 1 common thus the greatest common factor is 1