Question

Determine the GCF of 56f3g2 and 70fg3.

7fg^2

7f^3g^3

14fg^2

14f^3g^3

Answer 1

Answer:

Option C) $\text{GCF} = 14fg^2$

Step-by-step explanation:

We are given the following:

$56f^3g^2 \text{ and }70fg^3$

We have to find the greatest common factor of the two expressions.

We will use the technique of prime factorization to do so:

$56f^3g^2\\\\=2\times 2\times 2\times 7\times f\times f\times f\times g\times g\\\\70fg^3\\\\=2\times 5\times 7\times f\times g\times g\times g$

The common factors of both expressions are:

$\text{Common factors} = 2\times 7\times f\times g\times g$

Thus, the greatest common factor is:

$\text{GCF} = 14fg^2$

Option C) is the correct option.