Manhattan 5lb - Divisibility and Primes Q9

GRE Quant Problem Solving
1

Hi, for question 9 from chapter 13 of the book, the answer solution which I tried doing it by greg’s method is different from the book answer. Can someone clarify this?

The question is How many factors greater than 1 do 120, 210, and 270 have in common? The answer I got is 6(using primefactorization method) whereas the answer book shows is 7.

2

Prime factorization, 120 = 2^3 * 3 * 5 , 210 = 2 * 3 * 5 * 7 , 270 = 2 * 3^3 *5

So the common terms are = 2 * 3 * 5. According to Gregs method, we get (2)(2)(2) = 8 factors which includes also 1.

They have asked factors greater than 1. So 7