To find the Greatest Common Factor (GCF) of \(9a^2\) and \(6a^3\), follow these steps:

1. **Factorize the coefficients and variables:**
   - \(9a^2 = 3 \times 3 \times a \times a\)
   - \(6a^3 = 2 \times 3 \times a \times a \times a\)

2. **Identify the common factors:**
   - Common factor of coefficients: The common factor of 9 and 6 is 3.
   - Common factor of variables: The common factor of \(a^2\) and \(a^3\) is \(a^2\).

3. **Multiply the common factors:**
   - Coefficients: \(3\)
   - Variables: \(a^2\)

Therefore, the GCF of \(9a^2\) and \(6a^3\) is:

\[
\text{GCF} = 3 \times a^2 = 3a^2
\]

Would you like more details on this process or have any questions?

Here are some related questions you might find useful:

1. How do you find the GCF of three or more terms?
2. What is the Least Common Multiple (LCM) of \(9a^2\) and \(6a^3\)?
3. How do you simplify expressions using the GCF?
4. How can you apply the GCF in factoring polynomials?
5. What are the differences between GCF and LCM?

**Tip:** Always factorize completely to ensure you don't miss any common factors when finding the GCF.

Learn how to find the Greatest Common Factor (GCF) of 9a^2 and 6a^3 with a detailed, step-by-step solution. This problem covers key algebraic concepts such as factorization and properties of exponents, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation