What is the greatest common factor of 27x^3 and 18x^4?

1. Factor the coefficients into primes: 27 = 3 times 3 times 3, and 18 = 2 times 3 times 3. 2. Write the variable parts in expanded form: x cubed is x times x times x, and x to the fourth is x times x times x times x. 3. The common factors are two 3s from the coefficients and three x's from the variables, since x cubed has only three factors of x to share. 4. Multiply the common factors: 3 times 3 times x times x times x gives 9x cubed. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_