Question

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.

The greatest common factor of$\mathbf{8}\mathit{x}$and $\mathbf{4}{\mathit{x}}^{\mathbf{2}}$is$\underset{\mathbf{¯}}{\mathbf{4}\mathbf{x}}$.

Short answer

The given statement is true.

Step-by-step solution

Step 1. State the definition of GCF (Greatest Common Factor).

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y.

Step 2. State the methods to find GCF.

The GCF of two or more non-zero integers, x & y, is the greatest positive integer m, which divides both, x & y. The Greatest Common Factor is commonly known as GCF. To calculate GCF, there are three common ways: division, multiplication and prime factorization.

Step 3. Factorize the expressions.

Solving the monomials individually by factorizing them:

$\begin{array}{c}8x=2·2·2·x\\ 4x^2=2·2·x·x\end{array}$

The greatest common factor from the above factor is:

$2·2·x=4x$

Taking the common factors from the above factors, the result will be 4x.

Hence, the given statement is true.