What is the greatest common factor of 12a2 and 20ab ?(1 point) Responses 10a 10 a 4a 4 a 4ab 4 a b 4a2b

Answer 1

To find the greatest common factor (GCF) of the terms \(12a^2\) and \(20ab\), we start by factoring each term.

1. Factor 12 and 20:

   • The prime factorization of 12 is \(2^2 \times 3\).
   • The prime factorization of 20 is \(2^2 \times 5\).

2. Identify the common factors of the coefficients:

   • The common factor of \(12\) and \(20\) is \(2^2\), which is \(4\).

3. Factor the variables:

   • For \(a^2\) from \(12a^2\) and \(ab\) from \(20ab\), the common factor is \(a\) (since it has the lowest exponent).

4. Combine the common factors:

   • The GCF of the coefficients is \(4\) and the GCF of the variable parts is \(a\).
   • Therefore, the GCF of \(12a^2\) and \(20ab\) is \(4a\).

Thus, the greatest common factor is 4a.