One quick math question

[sunshinesmiles]

Hey guys,

 

I am new here :) I was looking for new resources for my upcoming GRE exam and i stumbled upon this great site.

 

So i have a question that I cant seem to figure out. If anyone gets it then can you please post how you derived your answer?

 

Ok so the question is

 

What is the greatest positive integer n such that 2^(n) is a factor of 12^(10)?

 

-the answer is 20.

 

Maybe I have become brain dead temporarily but i cant seem to figure this question out :(

[Olm]

Using the laws of exponents,

 

12^10 = 3^10*2^20

 

From there, we can see that a base 2 number's exponent can be brought up all the way to 20 to factor that expression.

 

Thus, n = 20.

 

QED

[philipe]

Using the laws of exponents,

 

12^10 = 3^10*2^20

 

Could you please explain this to me? Thank you!

[coyote]

Could you please explain this to me? Thank you!

 

12^10 = (3*4)^10

 

Thus 12^10 = 3^10 * (2^2)^10 = 3^10 * 2^(10*2) = 3^10 * 2^20.

[ (a^b)^c = a^(b*c) ]

 

Since 3^10 will not contain any even factor , the maximum possible power of 2 in 12^10 will be 2^20.

[philipe]

Thanks a lot, Coyote. You posts are really helping me a lot! =]

[coyote]

Thanks a lot, Coyote. You posts are really helping me a lot! =]

 

Welcome. Glad I could be of some help. :)

[sunshinesmiles]

Thanks guys, I dint realize my question was a repost of someone else's question, so apologies for the double post.