Question 27803
Find the greatest common factor for each of the following set of terms.

12a^3b^2, 18a^2b^3, 6a^4b^4

[Consider 12,18 and 6
12 = 1X2X2X3,  18 = 2X3X3  and 6 = 1X2X3
You observe that 2 is in 12, in 18 and in 6
Therefore 2 is a factor common to 12,18 and 6
You observe that 3 is in 12, in 18 and in 6
Therefore 3 is a factor common to 12,18 and 6
Now you  observe that    one 2 and one 3 are present in 12, in 18 and in 6
Therefore 2X3 is a factor common to 12,18 and 6
You observe that nothing  greater than 6 can be found common in all the given   three numbers.
Thus 6 is the greatest common factor of 12,18 and 6
Now Consider a^3b^2, a^2b^3, a^4b^4
From the  experience that we  have gained out of the above illustration, we observe that a^2b^2 is present in each of the three and no higher power of  a or b is found in all the three.]
[All that is  given  in brackets is for you  to talk to yourself and see and understand. But the answer you should present in one stroke as follows:]
To find the GCF of
12a^3b^2, 18a^2b^3, 6a^4b^4
Now 12a^3b^2, 18a^2b^3, 6a^4b^4
= (6x2)(a^2b^2)X(a), (6x3)(a^2b^2)X(b), (6x1)(a^2b^2)x(a^2b^2)
= (6a^2b^2)X(2a),(6a^2b^2)X (3b),(6a^2b^2)X(a^2b^2)
Therefore the GCF is (6a^2b^2)
Note: In each of the three quantities in  the final step the second part that is 2a and 3b and a^2b^2 
you do not have anything common other than 1.
That should be your visual clue