should i mention all the factors and compare which are common or can we do it by prime factorization

if it can be done using prime factorization please explain

The prime factorisation of 120 is 2x2x2x3x5, 210 is 2x3x5x7, and 270 is 2x3x3x3x5. Therefore, the greatest common factor is 2x3x5 = 30. So the number of common factors of 120, 210, 270 is the same as the factors of 30, which are 8. Now, the question is asking for factors greater than one, which would mean that the answer is 8 - 1 = 7.

ok, thank you got it.