It can be shown (see any book on number theory) that if \(\operatorname{gcd}(m, n)=1\) then \(\phi(m n)=\phi(m) \phi(n)\). Using this property, the property developed in the preceding problem, and the property that \(\phi(p)=p-1\) for \(p\) prime, it is straightforward to determine the value of \(\phi(n)\) for any \(n\). Determine the following:

a. \(\phi(41)\) b. \(\phi(27)\) c. \(\phi(231)\) d. \(\phi(440)\)