Solution to (a)

\(47 \times 49 = 48 \times 49 – 1\ times 49\)\( = 2352 – 49 = 2303\)

Solution to (b)

\(48 = 2^4 \times 3\) and \(49 = 7^2\) so \(2352 = 2^4 \times 3 \times 7^2\)

Solution to (c)

Since \(2352\) is a multiple of \(48\), it is also a multiple of \(24\). Therefore the remainder when \(2353\) is divided by \(24\) is \(1\), so the time will be \(4.14 \text{pm}\).