Question

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 1

Answer:

First option: $27$

Second option: $m$

Third option: $n^2$

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 $54mn^4$ and $27m^3n^2$, you can find the Greatest Common Factor using this procedure:

1. List the prime factors of each expression:

$54mn^4=2*3*3*3*m*n*n*n*n$

$27m^3n^2=3*3*3*m*m*m*n*n$

2. List the common factors and multiply them. Then:

$GCF=3*3*3*m*n^2\\\\GCF=27mn^2$

Therefore, $27$, $m$ and $n^2$ are part of the Greatest Common Factor.