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

First option:
`27`

Second option:
`m`

Third option:
`n^2`

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.