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Help: Factors problem !!

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by gmatmachoman » Sun Aug 15, 2010 3:40 am
How many factors does 36^2 have?


36^2 : {2*2*3*3} ^2
(2^4 ) * (3 ^4)

Total no of factors : (4+1) * (4+1)
: 5* 5 = 25
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by Brent@GMATPrepNow » Sun Aug 15, 2010 6:55 am
praveen_gmat wrote:How many factors does 36^2 have?

How to solve this quickly?

In general, we can say that if N = (p^a)(q^b)(r^c)..., where p, q, r etc are prime numbers, then the total number of positive divisors of N is equal to (a+1)(b+1)(c+1)...

Example: 14000 = (2^4)(5^3)(7^1)

So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) = 5x4x2=40
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