What is the greatest common factor of 20 and 27?

The greatest common factor of 20 and 27 is 1.

To answer this we must begin by factoring both 20 and 27:

The factor pairs of 20 are (1,20), (2,10), and (4,5). The prime facrorization is 2*2*5.

The factor pairs of 27 are (1,27), (3,9). The prime factorization is 3*3*3.

Now we look to see what factors are common, or what factors are in both trees? With these two numbers the only common factor and the greatest common factor are the same - 1.