To find the greatest common factor (GCF) of \(12a^2\) and \(20ab\), we can factor each term:
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Factor \(12a^2\):
- The prime factorization of 12 is \(2^2 \times 3\).
- Thus, \(12a^2 = 2^2 \times 3 \times a^2\).
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Factor \(20ab\):
- The prime factorization of 20 is \(2^2 \times 5\).
- Thus, \(20ab = 2^2 \times 5 \times a \times b\).
Now we can determine the GCF by taking the lowest power of each common factor.
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For the number part:
- The common factor of 12 and 20 in terms of prime factors is \(2^2\).
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For the variable \(a\):
- The lowest power of \(a\) in \(12a^2\) is \(a^2\) and in \(20ab\) it is \(a^1\). Thus, we take \(a^1\) (or \(a\)).
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The variable \(b\) appears only in \(20ab\) but not in \(12a^2\), so it cannot be included in the GCF.
Now, we combine the common factors: \[ \text{GCF} = 2^2 \times a^1 = 4a. \]
Thus, the greatest common factor of \(12a^2\) and \(20ab\) is \(4a\).
The correct response is: 4a.