Discussion
The sum of all the common factors of 36 and 48 (excluding 1) is
Answer: B
The sum is 27.
The common factors of two numbers are exactly the factors of their HCF. Since \(36 = 2^{2} \times 3^{2}\) and \(48 = 2^{4} \times 3\), the HCF is \(2^{2} \times 3 = 12\).
\[ \begin{aligned} \text{factors of } 12 &: 1, 2, 3, 4, 6, 12 \\ \text{sum excluding } 1 &= 2 + 3 + 4 + 6 + 12 \\ &= 27 \end{aligned} \]
28 is the sum with 1 included, the trap the bracket in the question warns against. 26 and 29 do not correspond to any set of common factors.
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