$$ imes $$ Find the greatest common factor of the exp $$ 18 y c^{4} $$ $$ 66 y^{5} c^{5} $$ $$ 42 y^{2} c^{4} $$

Question

$$ 	imes $$ Find the greatest common factor of the exp $$ 18 y c^{4} $$ $$ 66 y^{5} c^{5} $$ $$ 42 y^{2} c^{4} $$

UpStudy AI · Accepted Answer

To find the **Greatest Common Factor (GCF)** of the expressions:

$$
18 y c^{4}, \quad 66 y^{5} c^{5}, \quad 42 y^{2} c^{4}
$$

we need to determine the GCF for both the numerical coefficients and the variable parts separately.

### Step 1: GCF of Numerical Coefficients
The numerical coefficients are **18**, **66**, and **42**.

- **Factorize each number:**
  - $$ 18 = 2 \times 3^2 $$
  - $$ 66 = 2 \times 3 \times 11 $$
  - $$ 42 = 2 \times 3 \times 7 $$

- **Identify the common factors:**
  - All three numbers share the factors **2** and **3**.

- **Calculate the GCF:**
  - GCF $$ = 2 \times 3 = 6 $$

### Step 2: GCF of Variable Parts
Consider the variables $$ y $$ and $$ c $$ in each expression.

- **For $$ y $$:**
  - The exponents are **1**, **5**, and **2**.
  - The smallest exponent is **1**.
  - GCF for $$ y $$ is $$ y^1 = y $$.

- **For $$ c $$:**
  - The exponents are **4**, **5**, and **4**.
  - The smallest exponent is **4**.
  - GCF for $$ c $$ is $$ c^4 $$.

### Step 3: Combine GCFs
Multiply the numerical GCF with the variable GCFs:

$$
\text{GCF} = 6 \times y \times c^{4} = 6 y c^{4}
$$

**Final Answer:**  
The greatest common factor is $$ 6\, y\, c^{4} $$.
The greatest common factor is $$ 6\, y\, c^{4} $$.

\( \times \) Find the greatest common factor of the exp \( 18 y c^{4} \) \( 66 y^{5} c^{5} \) \( 42 y^{2} c^{4} \)