In how many ways can 378 mobile phones be shared equally among the students present in a classroom?

Question

Question

This question was previously asked in

RPF SI Previous Paper 1 (Held On: 5 Jan 2019 Shift 1)

Answer 1

Concept Used:

Number = a^p × b^q × c^r...

Total number of factors = (p + 1)(q + 1)(r + 1) ...

Total number of odd factors = (q + 1)(r + 1) ..., if 'a' is an even prime number

Here, a, b, c... etc., are prime numbers.

Calculation:

Prime factorization of 378:

378 = 2 × 3 × 3 × 3 × 7

378 = 2¹ × 3³ × 7¹

So, the total number of factors of 378

⇒ (1 + 1)(3 + 1)(1 + 1)

⇒ 2 × 4 × 2 = 16

Conclusion:

The number 378 can be divided equally among the students in 16 different ways, as it has 16 factors. So, your solution is correct.

Therefore, the required number of ways = 16.

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