Question

What is the greatest common factor of 12a2
and 20ab
?(1 point)
Responses

4a
4 a

4ab
4 a b

10a
10 a

4a2b

Answer 1

To find the greatest common factor (GCF) of the expressions \(12a^2\) and \(20ab\), we first need to determine the GCF of their numerical coefficients and then the GCF of the variable parts.

1. **Numerical coefficients:**
- The coefficients are 12 and 20.
- The factors of 12 are: 1, 2, 3, 4, 6, 12.
- The factors of 20 are: 1, 2, 4, 5, 10, 20.
- The common factors are: 1, 2, and 4.
- Therefore, the GCF of 12 and 20 is 4.

2. **Variable parts:**
- In \(12a^2\), the variable part is \(a^2\).
- In \(20ab\), the variable part is \(ab\).
- The common factor for the variable \(a\) is \(a\) (the lowest exponent of \(a\) is 1 in \(ab\)).
- The variable \(b\) is only present in \(20ab\), so it is not common.

3. **Combining the GCF of the numerical and variable parts:**
- The GCF is \(4 \cdot a = 4a\).

Thus, the greatest common factor of \(12a^2\) and \(20ab\) is **4a**.