Question

Factor Linear Expressions Quick Check
2 of 52 of 5 Items
Question
What is the greatest common factor of 12a2
and 20ab
?(1 point)
Responses

4a2b
4 a squared b

4ab
4 a b

4a
4 a

10a

Answer 1

To find the greatest common factor (GCF) of the expressions \( 12a^2 \) and \( 20ab \), we can start by identifying the GCF of the coefficients and the variable parts separately.

1. **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 greatest common factor of 12 and 20 is 4.

2. **Variables**:
- For \( a^2 \) and \( ab \), the GCF will be the lowest power of \( a \), which is \( a \).

Now, combine the GCF of the coefficients and the variables:
- GCF = \( 4 \cdot a = 4a \)

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

Thus, the correct response is:
**4a**.