identify the greatest common factor of $40w^{4}x^{3}z$ and $15a^{4}w^{2}$.

Explanation:

Step1: Find GCF of coefficients

Find GCF of 40 and 15. Prime - factorize: (40 = 2\times2\times2\times5) and (15 = 3\times5). So, GCF of 40 and 15 is 5.

Step2: Find GCF of variables with (w)

For (w^4) and (w^2), using the rule (GCF(w^m,w^n)=w^{\min(m,n)}), we have (GCF(w^4,w^2)=w^2).

Step3: Consider other variables

The first term has (x^3) and (z) and the second term has (a^4), which are not common to both terms.

Answer:

(5w^2)