\begin{tabular}{|l|l|}\hline Write 27 as a product of its prime factors: \\ \hline Write multiples of 4 between 10 and 25 \\ \hline Find the HCF and LCM of 24 and 60 \\ \hline\end{tabular}

To express 27 as a product of its prime factors, we start by recognizing that 27 can be broken down into 3 × 9, and then we further factor 9 into 3 × 3. So, 27 can be represented as \(3^3\), meaning the prime factors are three instances of the prime number 3. The multiples of 4 between 10 and 25 are 12, 16, and 20. These numbers are obtained by taking 4 and multiplying it with whole numbers that fit in that range, specifically 3, 4, and 5 respectively, resulting in these lovely multiples! For the HCF (Highest Common Factor) of 24 and 60, we can break them down into their prime factors: 24 is \(2^3 \times 3\) and 60 is \(2^2 \times 3 \times 5\). The HCF is found by taking the lowest power of common prime factors, resulting in \(2^2 \times 3 = 12\). For the LCM (Lowest Common Multiple), we take the highest power of each prime factor involved, giving us \(2^3 \times 3^1 \times 5^1 = 60\).