Question
What is the greatest common factor of 12a2
and 20ab
?(1 point)
Responses
10a
10 a
4ab
4 a b
4a
4 a
4a2b
and 20ab
?(1 point)
Responses
10a
10 a
4ab
4 a b
4a
4 a
4a2b
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the expressions \(12a^2\) and \(20ab\), we should first factor each term.
1. **Factor \(12a^2\)**:
- The number \(12\) can be factored into \(2^2 \cdot 3\).
- Therefore, \(12a^2 = 2^2 \cdot 3 \cdot a^2\).
2. **Factor \(20ab\)**:
- The number \(20\) can be factored into \(2^2 \cdot 5\).
- Therefore, \(20ab = 2^2 \cdot 5 \cdot a \cdot b\).
Next, we find the GCF by taking the lowest power of each common factor:
- For the coefficients:
- From \(12\) (which is \(2^2 \cdot 3\)) and \(20\) (which is \(2^2 \cdot 5\)), the GCF of \(12\) and \(20\) is \(2^2\) (or 4).
- For the variable \(a\):
- The lowest power of \(a\) between \(a^2\) and \(a\) is \(a^1\) (or \(a\)).
- The variable \(b\) appears only in \(20ab\) and not in \(12a^2\), so it is not included in the GCF.
Putting it all together, the GCF is:
\[
4a
\]
Thus, the answer is **4a**.
1. **Factor \(12a^2\)**:
- The number \(12\) can be factored into \(2^2 \cdot 3\).
- Therefore, \(12a^2 = 2^2 \cdot 3 \cdot a^2\).
2. **Factor \(20ab\)**:
- The number \(20\) can be factored into \(2^2 \cdot 5\).
- Therefore, \(20ab = 2^2 \cdot 5 \cdot a \cdot b\).
Next, we find the GCF by taking the lowest power of each common factor:
- For the coefficients:
- From \(12\) (which is \(2^2 \cdot 3\)) and \(20\) (which is \(2^2 \cdot 5\)), the GCF of \(12\) and \(20\) is \(2^2\) (or 4).
- For the variable \(a\):
- The lowest power of \(a\) between \(a^2\) and \(a\) is \(a^1\) (or \(a\)).
- The variable \(b\) appears only in \(20ab\) and not in \(12a^2\), so it is not included in the GCF.
Putting it all together, the GCF is:
\[
4a
\]
Thus, the answer is **4a**.