Question
find the greatest common factor 6t4,9t4,9t3,15t4
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the expressions \(6t^4\), \(9t^4\), \(9t^3\), and \(15t^4\), we can follow these steps:
1. **Find the GCF of the coefficients (numerical part)**:
- The coefficients are 6, 9, 9, and 15.
- The factors of each are:
- 6: \(1, 2, 3, 6\)
- 9: \(1, 3, 9\)
- 15: \(1, 3, 5, 15\)
- The common factors are \(1\) and \(3\). The greatest of these is \(3\).
2. **Determine the GCF of the variable part**:
- The variable parts are \(t^4\), \(t^4\), \(t^3\), and \(t^4\).
- The lowest power of \(t\) among these is \(t^3\).
3. **Combine the GCFs**:
- Therefore, the GCF of the entire set of expressions is:
\[
3t^3
\]
So, the greatest common factor of \(6t^4\), \(9t^4\), \(9t^3\), and \(15t^4\) is \(3t^3\).
1. **Find the GCF of the coefficients (numerical part)**:
- The coefficients are 6, 9, 9, and 15.
- The factors of each are:
- 6: \(1, 2, 3, 6\)
- 9: \(1, 3, 9\)
- 15: \(1, 3, 5, 15\)
- The common factors are \(1\) and \(3\). The greatest of these is \(3\).
2. **Determine the GCF of the variable part**:
- The variable parts are \(t^4\), \(t^4\), \(t^3\), and \(t^4\).
- The lowest power of \(t\) among these is \(t^3\).
3. **Combine the GCFs**:
- Therefore, the GCF of the entire set of expressions is:
\[
3t^3
\]
So, the greatest common factor of \(6t^4\), \(9t^4\), \(9t^3\), and \(15t^4\) is \(3t^3\).