Question 27803: Find the greatest common factor for each of the following set of terms.
12a^3b^2, 18a^2b^3, 6a^4b^4
Please help. I am completely lost.
Thank you so much.
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! 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
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