Question
Find the GCF (greatest common factor) of the following terms. \[ \left\{3 x y, 5 x^{3} y, 7 x^{2}\right\} \]
Ask by Schmidt Ortega. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The GCF is x.
Solution
To find the GCF (greatest common factor), examine the constants and variables in each term.
Terms: 3xy, 5x³y, and 7x².
1. Constants: The numbers are 3, 5, and 7. They have no common factor other than 1.
2. Variable x: The exponents are 1, 3, and 2. Use the smallest exponent, which is x¹ (or just x).
3. Variable y: The first two terms include y, but the third term does not include y. Since y isn't in every term, it is not part of the GCF.
Thus, the GCF is: x.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find the GCF of the terms \(3xy\), \(5x^3y\), and \(7x^2\), we start by identifying the coefficients and the variable parts. The coefficients are 3, 5, and 7. The GCF of these numbers is 1, since they do not share any common factor greater than 1. Next, we look at the variables: - For \(x\), the smallest exponent is 1 (from \(3xy\)). - For \(y\), the smallest exponent is also 1 (from both \(3xy\) and \(5x^3y\)). Putting it all together, the GCF of the three terms is: \[ 1 \cdot x^1 \cdot y^1 = xy. \] Therefore, the GCF of \(3xy\), \(5x^3y\), and \(7x^2\) is \(xy\).
