Manhatten 5lbs Question - Chpt 13 Q7

GRE Quant Problem Solving
1
  1. 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 22235
210 is 2357
270 is 2333*5

I used the property where we have 1 common 2, 1 common 3 and 1 common 5 and so the answer should be 222=6 so how is the answer 7?

2

2 x 2 x 2 = 8 but you’re said that the factors are needed to be greater than 1 hence, subtract 1 : 8-1 = 7