To find the greatest common factor (GCF) of the terms \(50x\) and \(-80y\), we focus on the numerical coefficients first.

1. The factors of 50 are: \(1, 2, 5, 10, 25, 50\)
2. The factors of 80 are: \(1, 2, 4, 5, 8, 10, 16, 20, 40, 80\)

The greatest common factor of 50 and 80 is 10.

Next, since the variables \(x\) and \(y\) are different and don't share any factors, the GCF only involves the numbers.

Thus, the GCF of \(50x\) and \(-80y\) is **10**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the GCF of \(30x\) and \(45y\)?
2. How do you find the GCF of three terms, like \(40x\), \(60y\), and \(80z\)?
3. What is the GCF of polynomials such as \(15x^2 - 25x\)?
4. Can the GCF of two terms ever be a variable?
5. How is the GCF used when factoring expressions?

**Tip:** Always check the coefficients and variables separately when finding the GCF of algebraic terms.

Discover how to find the greatest common factor (GCF) of 50x and -80y using the factors of their numerical coefficients. This algebra problem demonstrates how to handle terms with different variables. Suitable for students in Grades 6-8.

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