Questions: Find the greatest common factor of these three expression 14, 12x^4, and 4x^3

Transcript text: Find the greatest common factor of these three expression $14,12 x^{4}$, and $4 x^{3}$

Solution

Solution Steps

To find the greatest common factor (GCF) of the given expressions, we need to identify the common factors in both the numerical coefficients and the variable parts. For the numerical coefficients, we find the GCF of 14, 12, and 4. For the variable parts, we look for the lowest power of $x$ that appears in all terms.

Step 1: Identify the Coefficients

The given expressions are $14$, $12x^4$, and $4x^3$. We first identify the numerical coefficients: $14$, $12$, and $4$.

Step 2: Calculate the GCF of the Coefficients

To find the greatest common factor (GCF) of the coefficients $14$, $12$, and $4$:

The prime factorization of $14$ is $2 \times 7$.
The prime factorization of $12$ is $2^2 \times 3$.
The prime factorization of $4$ is $2^2$.

The GCF of the coefficients is $2$.

Step 3: Determine the Variable Part

Next, we look at the variable parts of the expressions. The powers of $x$ are $0$ (from $14$), $4$ (from $12x^4$), and $3$ (from $4x^3$). The minimum power of $x$ is $0$.

Step 4: Construct the GCF Expression

Since the minimum power of $x$ is $0$, the GCF expression consists only of the numerical GCF. Therefore, the GCF of the expressions $14$, $12x^4$, and $4x^3$ is $2$.

Final Answer

$\boxed{2}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!