What is the total number of positive integers that are less

Basically the question asks about the total no of co-prime factors of 100. Bunuel has already explained the method, however, for just knowing something new, there is another method to do this :

100 = Find out all the prime factors = 2 and 5. Thus total no of co-prime integers to 100, and less than 100 = (1-1/2)(1-1/5)*100 = 1/2*4/5*100 = 40.

So, if I have to find out the total no of co-prime factors for 48, that would be -->

Total prime factors of 48 = 2,3. Thus the co=prime factors less than 48 = (1-1/2)(1-1/3)*48 = 1/2*2/3*48 = 16. This includes 1, which is co-prime to 48.

This is not some thumb rule, there is a proper derivation for this.Though, it is beyond the scope of GMAT.