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To find the greatest common factor (GCF) of the two expressions \( 28u^8 x^6 y^5 \) and \( 24u^3 y^2 \), we will follow these steps:

### Step 1: Find the GCF of the coefficients
The coefficients are 28 and 24. To find their GCF:

- The prime factorization of 28 is \( 2^2 \times 7 \).
- The prime factorization of 24 is \( 2^3 \times 3 \).

The common prime factor is \( 2^2 \). So, the GCF of 28 and 24 is \( 4 \).

### Step 2: Find the GCF of the variables
For the variables \( u \), \( x \), and \( y \):

- \( u \)-terms: The powers of \( u \) in the expressions are \( u^8 \) and \( u^3 \). The GCF is \( u^3 \) (the lower power).
- \( x \)-terms: The powers of \( x \) are \( x^6 \) and (there's no \( x \) in the second expression). So, there’s no common factor involving \( x \).
- \( y \)-terms: The powers of \( y \) are \( y^5 \) and \( y^2 \). The GCF is \( y^2 \).

### Step 3: Combine the results
Now, combine the GCF of the coefficients and the variables. The GCF of the two expressions is:

\[
4u^3 y^2
\]

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you find the least common multiple (LCM) of two expressions like these?
2. What is the prime factorization of larger numbers, and how can it help in finding the GCF?
3. How does the GCF of polynomials differ from that of constants?
4. Can the GCF method be applied when dealing with negative coefficients? If yes, how?
5. How does factoring expressions help in simplifying algebraic equations?

**Tip:** When finding the GCF of algebraic expressions, always use the smallest powers of each variable common to both expressions.

Find the greatest common factor (GCF) of the two expressions 28u^8 x^6 y^5 and 24u^3 y^2.

Learn how to find the greatest common factor (GCF) of two algebraic expressions, 28u^8x^6y^5 and 24u^3y^2. This step-by-step guide covers GCF calculations for both coefficients and variables, including prime factorization and exponent rules. Suitable for Grades 9-11.

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