In how many ways can 648 mobiles be distributed equally to the students of a class?

Given:

Total number of mobiles = 648

Formula Used:

Number of ways to distribute mobiles equally = Total number of mobiles / Total number of students

Calculation:

We need to find a number that divides 648 exactly (i.e., without leaving a remainder) and matches one of the given options.

Factors of 648: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648

Thus, the required number of mobile phones to be shared equally among the students = 20

The correct answer is option (1).

Shortcut Trick

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3

⇒ 648 = 2³ × 3⁴

Thus, the required number of mobile phones to be shared equally among the students = (3 + 1)(4 + 1) = 4 × 5 = 20.

Hence, The correct answer is option (1).