Final answer:
The greatest common factor (GCF) of monomials is found by identifying the highest power of each variable that is present in all monomials along with the largest number that divides each coefficient without a remainder.
Step-by-step explanation:
To find the greatest common factor (GCF) of monomials, we need to identify the highest factor that divides each term without any remainder. We look for the highest exponent common to each variable in all monomials and the largest number that is a factor of each coefficient.
Let's assume the monomials in question are not given, but to find the GCF, you would follow these steps:
- Factorize each coefficient into its prime factors.
- List out all variables with their lowest exponents found in the monomials.
- Multiply the common prime factors with the common variables and their lowest exponents.
For instance, if we had monomials 60x^3y^2 and 45x^2y^4, the GCF would be calculated by identifying the highest power of x and y that is present in both, which is x^2y^2, and the largest number that divides both 60 and 45 without a remainder, which is 15. So, the GCF would be 15x^2y^2.