To find the greatest common factor (GCF) of the two terms \( 54x \) and \( 18y^3 \), follow these steps:

1. **Factor the numerical coefficients**:
   - \( 54 = 2 \times 3^3 \)
   - \( 18 = 2 \times 3^2 \)

   The GCF of 54 and 18 is \( 2 \times 3^2 = 18 \).

2. **Factor the variable parts**:
   - \( 54x \) has the variable \( x \).
   - \( 18y^3 \) has the variable \( y^3 \).

   Since there are no common variables between \( x \) and \( y^3 \), no variables contribute to the GCF.

3. **Conclusion**:
   The GCF of \( 54x \) and \( 18y^3 \) is \( 18 \).

### Final answer: \( 18 \)

Would you like further details on the process or any clarification?

Here are 5 related questions:
1. What is the GCF of \( 36x^2 \) and \( 48y \)?
2. How do you find the least common multiple (LCM) of \( 54x \) and \( 18y^3 \)?
3. What happens if both terms share a variable in their GCF?
4. Can the GCF include variables like \( x \) or \( y \)?
5. How would the GCF change if the expressions were \( 54x^2 \) and \( 18x^3y^3 \)?

**Tip**: Always factor both the numerical coefficients and the variables separately to find the GCF.

Learn how to find the greatest common factor (GCF) of 54x and 18y^3 with a clear step-by-step solution. This problem covers key algebraic concepts such as factoring numerical coefficients and identifying the GCF of algebraic terms. Suitable for students in Grades 7-9.

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