Find the greatest common factor of the expressions $15a{b}^2$ and $45a^2{b}^3$ .

A) $15a{b}^2$
B) $675a{b}^2$
C) $675a^3{b}^5$
D) $15a^3{b}^5$
E) $675a^2{b}^3$

The greatest common factor (GCF) of two expressions is found by taking the lowest power of common factors. Here, the GCF is $15a{b}^2$ because both expressions share at least $15$ as a coefficient, at least one $a$ , and at least two $b$ 's, making $15a{b}^2$ the largest expression that divides both given expressions.