How can 675 mobile phones be shared in an evenly similar manner in the students present in the class?
12
The intended meaning: in how many ways can 675 mobile phones be distributed equally among the students of a class? Each way corresponds to a number of students that divides 675 exactly, so we count the factors of 675.
Prime factorisation: \(675 = 3^3 \times 5^2\).
Number of factors = \((3 + 1)(2 + 1) = 4 \times 3 = 12\).
These are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225 and 675.
Hence, the phones can be shared equally in 12 ways.
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