Question
Question
What is the greatest common factor of 10x6y4
and 20x7y8
?(1 point)
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the expressions \(10x^6y^4\) and \(20x^7y^8\), we will follow these steps:
1. **Find the GCF of the numerical coefficients**:
- The coefficients are 10 and 20.
- The GCF of 10 and 20 is 10.
2. **Find the GCF of the \(x\) terms**:
- The terms are \(x^6\) and \(x^7\).
- The GCF is \(x^{\min(6, 7)} = x^6\).
3. **Find the GCF of the \(y\) terms**:
- The terms are \(y^4\) and \(y^8\).
- The GCF is \(y^{\min(4, 8)} = y^4\).
4. **Combine the results**:
- Now, we combine the GCF of the coefficients and the variables.
- The GCF of \(10x^6y^4\) and \(20x^7y^8\) is \(10x^6y^4\).
Therefore, the greatest common factor is **\(10x^6y^4\)**.
1. **Find the GCF of the numerical coefficients**:
- The coefficients are 10 and 20.
- The GCF of 10 and 20 is 10.
2. **Find the GCF of the \(x\) terms**:
- The terms are \(x^6\) and \(x^7\).
- The GCF is \(x^{\min(6, 7)} = x^6\).
3. **Find the GCF of the \(y\) terms**:
- The terms are \(y^4\) and \(y^8\).
- The GCF is \(y^{\min(4, 8)} = y^4\).
4. **Combine the results**:
- Now, we combine the GCF of the coefficients and the variables.
- The GCF of \(10x^6y^4\) and \(20x^7y^8\) is \(10x^6y^4\).
Therefore, the greatest common factor is **\(10x^6y^4\)**.