Determine which of the following expressions are part of the greatest common factor of 54mn4 and 27m3n2. Select all situations that apply. 27 m n2 18 9

Answer: First option: [tex]27[/tex] Second option: [tex]m[/tex] Third option: [tex]n^2[/tex] Step-by-step explanation: By definition, the Greatest Common Factor (GCF) is the greatest factor that divides two or more numbers with zero remainder. Given the expressions [tex]54mn^4[/tex] and [tex]27m^3n^2[/tex], you can find the Greatest Common Factor using this procedure: 1. List the prime factors of each expression: [tex]54mn^4=2*3*3*3*m*n*n*n*n[/tex] [tex]27m^3n^2=3*3*3*m*m*m*n*n[/tex] 2. List the common factors and multiply them. Then: [tex]GCF=3*3*3*m*n^2\\\\GCF=27mn^2[/tex] Therefore, [tex]27[/tex], [tex]m[/tex] and [tex]n^2[/tex] are part of the Greatest Common Factor.