How can the 648 mobile phones be distributed in an evenly similar manner in the students present in the class?
20
The garbled stem asks: in how many ways can 648 mobile phones be distributed equally among the students of a class? Each possible class size must divide 648 exactly, so we need the number of divisors of 648.
Prime factorisation: \(648 = 8 \times 81 = 2^{3} \times 3^{4}\).
Number of divisors \(= (3 + 1)(4 + 1) = 4 \times 5 = 20\).
Hence, 648 phones can be distributed equally in 20 ways.
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