In how many ways can 936 mobiles be distributed equally among the students of…

Concept:

For a positive integer expressed as a product of prime powers, the total number of positive divisors equals the product of (each prime's exponent + 1) taken across all its distinct prime factors. Splitting a quantity of identical items into equal-sized groups is possible in exactly as many ways as that quantity has positive divisors — each divisor gives a valid group size (equivalently, a valid number of students).

Application:

1. Factorize 936 into prime powers: 936 = 23 × 32 × 131.

2. Apply the divisor-count rule using each prime's exponent: (3 + 1) × (2 + 1) × (1 + 1).

3. Multiply out: 4 × 3 × 2 = 24.

Cross-check:

Independent check: 23 × 32 × 131 = 8 × 9 × 13 = 936, confirming the factorization is correct, and the exponent-based product consistently gives 24 — matching the divisor tally.

Answer: There are 24 ways to distribute 936 mobiles equally among the students of a class — one way for each positive divisor of 936.