QuestionPart B What is the GCF of $8 x y$ and $12 x$ ?

Studdy Solution

STEP 1

1. We are asked to find the greatest common factor (GCF) of two algebraic expressions: $8xy$ and $12x$ .
2. The GCF is the largest expression that divides both given expressions without leaving a remainder.

STEP 2

1. Factor each expression into its prime factors.
2. Identify the common factors.
3. Determine the GCF by multiplying the lowest power of all common factors.

STEP 3

Factor each expression into its prime factors.
For $8xy$ : - The number 8 can be factored into primes as $2^3$ . - The expression includes the variables $x$ and $y$ .
Thus, the prime factorization of $8xy$ is $2^3 \cdot x \cdot y$ .
For $12x$ : - The number 12 can be factored into primes as $2^2 \cdot 3$ . - The expression includes the variable $x$ .
Thus, the prime factorization of $12x$ is $2^2 \cdot 3 \cdot x$ .

STEP 4

Identify the common factors.
- Both expressions have the factor $2$ in common. - Both expressions have the variable $x$ in common.

STEP 5

Determine the GCF by multiplying the lowest power of all common factors.
- The lowest power of the common factor $2$ is $2^2$ . - The lowest power of the common factor $x$ is $x^1$ .
Thus, the GCF is:
$2^2 \cdot x = 4x$
The greatest common factor of $8xy$ and $12x$ is:
$\boxed{4x}$

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