Question
Find the greatest common factor.'
6n^2,8n^2
6n^2,8n^2
Answers
GPT-4o mini
To find the greatest common factor (GCF) of \( 6n^2 \) and \( 8n^2 \), we start by determining the GCF of the coefficients and the variable parts separately.
1. **Coefficients:** The coefficients are 6 and 8.
- The factors of 6 are: 1, 2, 3, 6
- The factors of 8 are: 1, 2, 4, 8
- The common factors are: 1, 2
- The greatest common factor of 6 and 8 is **2**.
2. **Variable Part:** Both terms have \( n^2 \).
- The GCF of \( n^2 \) and \( n^2 \) is \( n^2 \).
Now, we combine the GCF of the coefficients with the GCF of the variable parts.
So, the greatest common factor of \( 6n^2 \) and \( 8n^2 \) is:
\[
GCF = 2n^2
\]
Thus, the greatest common factor is \( \boxed{2n^2} \).
1. **Coefficients:** The coefficients are 6 and 8.
- The factors of 6 are: 1, 2, 3, 6
- The factors of 8 are: 1, 2, 4, 8
- The common factors are: 1, 2
- The greatest common factor of 6 and 8 is **2**.
2. **Variable Part:** Both terms have \( n^2 \).
- The GCF of \( n^2 \) and \( n^2 \) is \( n^2 \).
Now, we combine the GCF of the coefficients with the GCF of the variable parts.
So, the greatest common factor of \( 6n^2 \) and \( 8n^2 \) is:
\[
GCF = 2n^2
\]
Thus, the greatest common factor is \( \boxed{2n^2} \).