(a) Both \(24\) and \(39\) are divisible by \(3\text{,}\) and \(3\) and \(5\) have no common factors, so we get

\begin{equation*} 8 \equiv 13 \pmod 5\text{.} \end{equation*}

(b) Again, we can divide by 3. However, doing so blindly gives us \(8 \equiv 13 \pmod{15}\) which is no longer true. Instead, we must also divide the modulus 15 by the greatest common factor of \(3\) and \(15\text{,}\) which is \(3\text{.}\) Again we get

\begin{equation*} 8 \equiv 13 \pmod 5\text{.} \end{equation*}