Question

Melissa says the GCF of 8x2y + 4xy is 4. Adam says the GCF is 4y. Erica says the GCF is 4xy. Who is correct? In complete sentences explain your answer, and factor the expression.

Answer 1

Erica

Explanation:

The given expression is
`8x^2y+4xy`.

The prime factorization of the first term is

`8x^2y=2^3\cdot x^2\cdot y`

The prime factorization of the second term is

`4xy=2^2\cdot x\cdot y`

The greatest common factor is product of the least powers of the common factors.

`GCF=2^2\cdot x\cdot y=4xy`

Therefore Erica is correct.