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by liferocks » Tue Jun 08, 2010 11:39 pm
36=2^2 * 3^2
so 36^2=2^4 * 3^4
number of factors = (4+1)*(4+1)=25
option D
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by dkumar.83 » Tue Jun 08, 2010 11:56 pm
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?
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by gmatmachoman » Wed Jun 09, 2010 12:16 am
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!!
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by liferocks » Wed Jun 09, 2010 12:38 am
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)...
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by The Jock » Wed Jun 09, 2010 12:42 am
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/
Thanks and Regards,
Varun
https://mbayogi.wordpress.com/
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by dkumar.83 » Wed Jun 09, 2010 1:36 am
Thanks for the explanation.
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by Thouraya » Wed Jun 09, 2010 3:13 am
Hey,

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


Thank you!
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by liferocks » Wed Jun 09, 2010 3:28 am
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)...
"If you don't know where you are going, any road will get you there."
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by hardik.jadeja » Thu Jun 10, 2010 6:54 am
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. :D

Hope that helps.
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