Let's focus first on the coefficients. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 42 are 1, 2, 3, 6, 7, 14, 21. So the "common factors" are 1, 2, 3, and 6. So the GCF is 6.
The GCF for variables is to select the smallest value of degree (or power).
The GCF of x^5 and x^3 is x^3.
The GCF of y^3 and y^2 is y^2.
The GCF of z^2 and z is z.
Combining together: 6 x^3 y^2 z.
