VJesus12 wrote:How many factors does 36^2 have?

A. 2
B. 8
C. 24
D. 25
E. 26

The OA is the option D.

How can I solve this question is a fast way? Can anyone give me a good explanation? Thanks.

-------ASIDE-------------------
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
---NOW ONTO THE QUESTION-----------------

36 = (2)(2)(3)(3)
So, 36² = (36)(36)
= (2)(2)(3)(3)(2)(2)(3)(3)
= (2^4)(3^4)
So, the number of positive divisors of 36² = (4+1)(4+1)
= (5)(5)
= 25

Answer: D

Cheers,
Brent