What is the greatest common factor or 12a and 9a^2

The factors of 9 are 1, 3 and 9.

The factors of 12 are 1, 2, 3, 4, 6 and 12.

The factor of a and a^2 is just "a."

For coefficients, the common factors of 9 and 12 are 1 and 3 only. But the greatest common factor is 3.

For variables, the greatest factor is just also "a."

Multiplying these two factors, we get the answer: 3a