How many factors does the number 12288 have?

Correct option is D

Given:

Number = 12288

Concept Used:​

If N = $$a^p \times b^q \times c^r\times d^s.......,$$

Total Numbers of factors 

= (p +1) $$\times$$ (q + 1) $$\times$$ (r + 1) $$\times$$ (s + 1)..........

Solution:

​First, we find the prime factorization of 12288.

12288 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

So, 12288 = $$2^{12} × 3^1$$​​

Number of factors = (12 + 1) × (1 + 1) = 13 × 2 = 26

The number 12288 has 26 factors.