Two integers are said to be relatively prime if they share no common factors, that is if there is no integer greater than 1 that divides evenly into both of them. Note that 1 is relatively prime to all integers. Let $\varphi(n)$ be the number of integers less than n that are relatively prime to n$. Since \varphi(m n)=\varphi(m) \varphi(n)$ for $m$ and $n$ relatively prime, we have $\varphi(2001)=\varphi(3 \cdot 23 \cdot$ 29)=(3-1)(23-1)(29-1)=1232$.