Final answer:
The greatest common factor of the monomials 25x⁵ and 20x⁶ is 5x⁵, which comprises the highest common numerical factor, 5, and the smallest common exponent for 'x', which is 5.
Step-by-step explanation:
To find the greatest common factor (GCF) of the monomials 25x⁵ and 20x⁶, we need to determine the highest exponent of 'x' that is common to both monomials and the largest factor that can divide both of the coefficients 25 and 20 without leaving a remainder. First, let's find the GCF of the numerical coefficients.
The factors of 25 are 1, 5, and 25, and the factors of 20 are 1, 2, 4, 5, 10, and 20. The largest common factor of 25 and 20 is 5. Now, we look at the variable part. The variable 'x' to the lesser exponent in both terms is x⁵. Therefore, the GCF of 25x⁵ and 20x⁶ is 5x⁵.