factors

[dkumar.83]

Is there any shortcut to find this answer?

[liferocks]

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

[dkumar.83]

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?

[gmatmachoman]

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!!

[liferocks]

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)...

[The Jock]

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/

[dkumar.83]

Thanks for the explanation.

[Thouraya]

Hey,

Is it a rule that to know the number of factors we take the exponent and add 1 to it?


Thank you!

[liferocks]

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)...

[hardik.jadeja]

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.