# 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

So,

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

So,

The GCF is 2 × 2 × x × x = 4x2

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

So,

Thus, the GCF for 15x4, 25x3, and 75x5 is 5 × x × x × x = 5x3

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