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


common factor of 12 and 20
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 12x2 and 20x4


common factor of 12x^2 and 20 x^4
The GCF is 2 × 2 × x × x = 4x2

Find the GCF for 15x4, 25x3, and 75x5


common factor of  15x^4, 25x^3, and 75x^5
Thus, the GCF for 15x4, 25x3, and 75x5 is 5 × x × x × x = 5x3

Finding the greatest common factor quiz. See how well you understand this lesson.

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