WHat is the greatest common factor of 12a^2 and 20ab?

Answer 1

To find the greatest common factor (GCF) of the expressions \(12a^2\) and \(20ab\), we can follow these steps:

1. Factor the coefficients:

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

2. Find the GCF of the coefficients:

   • The common factors of 12 and 20 are \(2^2\).
   • Therefore, the GCF of the coefficients (12 and 20) is \(4\).

3. Consider the variable parts:

   • For \(a^2\) and \(ab\), the common variable factor is the lowest power of \(a\): \(a^1 = a\).
   • There is no common factor for \(b\) in \(a^2\) because \(b\) does not appear there.

4. Combine the GCF of the coefficients and the variables:

   • The overall GCF is \(4a\).

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