28v^8w^7 and 8y^4v^6w^3 find greatest common factor

To find the greatest common factor (GCF) of the two terms \( 28v^8w^7 \) and \( 8y^4v^6w^3 \), follow these steps:

### 1. Coefficients:
- The GCF of the coefficients 28 and 8 is the largest number that divides both:
  \[
  \text{GCF}(28, 8) = 4
  \]

### 2. Variables:
- **For \( v \):** The powers of \( v \) are 8 and 6. The GCF of \( v^8 \) and \( v^6 \) is \( v^6 \) (smallest power).
- **For \( w \):** The powers of \( w \) are 7 and 3. The GCF of \( w^7 \) and \( w^3 \) is \( w^3 \) (smallest power).
- **For \( y \):** There is no \( y \) in the first term, so no contribution from \( y \).

### Final GCF:
\[
\text{GCF} = 4v^6w^3
\]

Would you like further details or have any questions?

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Here are 5 related questions to extend your learning:

1. How do you find the greatest common factor of more complex expressions with multiple variables?
2. How does the GCF help when simplifying algebraic expressions?
3. What is the role of prime factorization in finding the GCF of two numbers?
4. Can you find the least common multiple (LCM) of \( 28v^8w^7 \) and \( 8y^4v^6w^3 \)?
5. How would the GCF change if the powers of \( y \) were present in both terms?

**Tip:** Always remember, for variables, the GCF takes the smallest exponent that appears in all terms.

Learn how to find the greatest common factor (GCF) of two algebraic terms: 28v^8w^7 and 8y^4v^6w^3. This problem breaks down how to find the GCF of coefficients and variables with exponents, covering key algebraic concepts for students in Grades 9-10.

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