Is there any shortcut to find this answer?

36=2^2 * 3^2 so 36^2=2^4 * 3^4 number of factors = (4+1)*(4+1)=25 option D

Thanks for the prompt reply. Just to add, incase the question asks the number of factors of 36*96, then what will be the answer?

dkumar.83 wrote:Thanks for the prompt reply. Just to add, incase the question asks the number of factors of 36*96, then what will be the answer? 36 * 96 = 6 * 6 * 6 * 16 = 2 * 3 * 2 * 3 * 2*3 * 2^4 = 2^7 *3 ^3 = No of factors : (7+1) * (3+1) 8 * 4 = 32 Hope this helps!!

gmatmachoman wrote:dkumar.83 wrote:Thanks for the prompt reply. Just to add, incase the question asks the number of factors of 36*96, then what will be the answer? 36 * 96 = 6 * 6 * 6 * 16 = 2 * 3 * 2 * 3 * 2*3 * 2^4 = 2^7 *3 ^3 = No of factors : (7+1) * (3+1) 8 * 4 = 32 Hope this helps!! just to generalize for any number n=a^p *b^q..so on where a,b ..etc are prime number of factors is (p+1)(q+1)...

Hey dkumar.83, I have given a full explanation on this topic in one of my post in my blog. I am sure that you would like to have a look at it. Finding the number of factors(or divisors) of a given number(composite number): https://mbayogi.wordpress.com/2010/04/28 ... tics-gyan/

Hey, Is it a rule that to know the number of factors we take the exponent and add 1 to it? Thank you!

Thouraya wrote:Hey, Is it a rule that to know the number of factors we take the exponent and add 1 to it? Thank you! yes. for any number n=a^p *b^q..so on where a,b ..etc are prime number of factors is (p+1)(q+1)...

Guys, there is a simple rule that a perfect square will always have odd number of factors. Only option D is odd. Rest all are even. Absolutely no calculations required. Hope that helps.