Math Problem Statement

Find the GCF of 9a^2 and 6a^3

Solution

To find the Greatest Common Factor (GCF) of 9a29a^2 and 6a36a^3, follow these steps:

  1. Factorize the coefficients and variables:

    • 9a2=3×3×a×a9a^2 = 3 \times 3 \times a \times a
    • 6a3=2×3×a×a×a6a^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 a2a^2 and a3a^3 is a2a^2.
  3. Multiply the common factors:

    • Coefficients: 33
    • Variables: a2a^2

Therefore, the GCF of 9a29a^2 and 6a36a^3 is:

GCF=3×a2=3a2\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 9a29a^2 and 6a36a^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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Greatest Common Factor (GCF)
Factorization

Formulas

GCF Formula: GCF(a^m, b^n) = Common Factor of Coefficients × Common Factor of Variables

Theorems

Fundamental Theorem of Arithmetic
Properties of Exponents

Suitable Grade Level

Grades 7-9