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

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 \( 6\, y\, c^{4} \).