\( 27 y \) and \( 54 y^{3} \)

It looks like you've provided two algebraic expressions: - \( 27y \) - \( 54y^{3} \) Assuming you want to **find the Greatest Common Factor (GCF)** of these two expressions, here's how you can do it: ### Step 1: Factor Each Term into Its Prime Factors 1. **Factor 27y:** \[ 27y = 3 \times 3 \times 3 \times y = 3^{3} \times y \] 2. **Factor 54y³:** \[ 54y^{3} = 2 \times 3 \times 3 \times 3 \times y \times y \times y = 2 \times 3^{3} \times y^{3} \] ### Step 2: Identify the Common Factors - **Numerical Factors:** - Both terms have \( 3^{3} \) as a common numerical factor. - **Variable Factors:** - Both terms have \( y \) as a common variable factor. - The smallest power of \( y \) present in both terms is \( y \). ### Step 3: Multiply the Common Factors to Find the GCF \[ \text{GCF} = 3^{3} \times y = 27y \] ### Conclusion The **Greatest Common Factor (GCF)** of \( 27y \) and \( 54y^{3} \) is **\( 27y \)**. ### Additional: Factoring Each Expression If you're interested in fully factoring each expression, here's how you can do it: 1. **Factor \( 27y \):** \[ 27y = 3^{3} \times y \] 2. **Factor \( 54y^{3} \):** \[ 54y^{3} = 2 \times 3^{3} \times y^{3} \] This can be useful for simplifying expressions, solving equations, or performing operations like addition and subtraction with these terms. --- If you had a different intention with these expressions, please provide more details so I can assist you accordingly!