What is the greatest common factor of 12a^2

Question

and 20ab
?(1 point)
Responses

4a
4 a

4ab
4 a^2 b

10a
10 a

4a2b

Answer 1

To find the greatest common factor (GCF) of \( 12a^2 \) and \( 20ab \), we first break down 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 GCF of 12 and 20 is 4.

2. Variable part: Now, for the variable parts:

   • For \( 12a^2 \), we have \( a^2 \).
   • For \( 20ab \), we have \( ab \).
   • The common factor for \( a^2 \) and \( ab \) is \( a \) (since the lower power of \( a \) is 1).

Combining the GCF of the coefficients (4) and the GCF of the variable parts (\( a \)), we get:

\[ \text{GCF} = 4a \]

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