- How many factors greater than 1 do 120, 210, and 270 have in common?

The answer in 7

Without listing the factors how could I calculate this quicker.

120 is 2*2*2*3*5

210 is 2*3*5*7
270 is 2*3

*3*3*5

I used the property where we have 1 common 2, 1 common 3 and 1 common 5 and so the answer should be 2*2*2=6 so how is the answer 7?