Identify the greatest common factor of 12a^4b^7 and 18a^5b^3 .
The prime factorization of 12 is 2^2 * 3. The prime factorization of 18 is 2 * 3^2.
The prime factorization of a^4 is a * a * a * a. The prime factorization of a^5 is a * a * a * a * a.
The prime factorization of b^7 is b * b * b * b * b * b * b. The prime factorization of b^3 is b * b * b.
To find the greatest common factor, we need to find the highest power of each number and variable that both terms have in common.
The GCF of 12a^4b^7 and 18a^5b^3 is 2 * 3 * a^4 * b^3.
So, the greatest common factor is 6a^4b^3. Answer: \boxed{6a^4b^3}.