Final answer:
To find the greatest common factor of 6c^5 and 15c^6, find the largest number that divides both numerical coefficients (which is 3) and the smallest exponent of 'c' (which is c^5), resulting in a GCF of 3c^5.
Step-by-step explanation:
The greatest common factor (GCF) of the monomials 6c5 and 15c6 can be found by identifying the greatest factor that divides both numbers and the smallest exponent of the common variables. To find the GCF of the numerical coefficients (6 and 15), we look for the largest number that divides both without a remainder, which is 3. Since the variables are both 'c', we take the one with the smallest exponent, which is c5. Therefore, the GCF is 3c5.