Finding the greatest common factor
In
greatest common factor,
finding the greatest common factor of number was the goal.
Here, we will do the same thing, but we will take the concept to the next level.
Recall that if you are looking for the GCF for 12 and 20, we need first to factor each number into its prime factorization as shown below.
As you can see, 2 × 2 = 4 is the greatest factor 12 and 20 have in common, so it is the GCF
Find GCF for 12x
^{2} and 20x
^{4}
So,
The GCF is 2 × 2 × x × x = 4x
^{2}
Find the GCF for 15x
^{4}, 25x
^{3}, and 75x
^{5}
So,
Thus, the GCF for 15x
^{4}, 25x
^{3}, and 75x
^{5} is 5 × x × x × x = 5x
^{3}
Finding the greatest common factor quiz. See how well you understand this lesson.

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