Problem Solving

Can't crack it. Please help:

The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number then f(p) =

A) p - 1
B) p - 2
C) (p+1)/2
D) (p-1)/2
E) 2

Correct answer is A). Thank you!
yeah - it's CAT2

For a prime number k, there is no factor p such that 1<p<k

so f(3)= 1,2 hence 2
f(5)=1,2,3,4 hence 4 and so on

thus the f(p) would always be p-1

THank you 800GMAT. This one is rough. The wording is so confusing.