Brain Teasers
Number of Divisors
We call a positive integer a "good number", if the product of all its divisors equals its cube.
For example, 12 is a good number, because the divisors of 12 are 1, 2, 3, 4, 6, 12, and 1*2*3*4*6*12=1728=12^3.
If n is a good number, what is the minimum number of divisors that n^2 has?
For example, 12 is a good number, because the divisors of 12 are 1, 2, 3, 4, 6, 12, and 1*2*3*4*6*12=1728=12^3.
If n is a good number, what is the minimum number of divisors that n^2 has?
Hint
It looks like a math teaser, but look at its category.If your answer is 11, then you're tricked.
Answer
Only one, because 1 is a good number!Hide Hint Show Hint Hide Answer Show Answer
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Comments
I don'y get it.
Got it on my first try!
Good one!
Category helps a lot too, thanks!
Good one!
Category helps a lot too, thanks!
SO CLOSE! infuriated!! but really fun!
could somebody explain?
Easy!
This should be in the math category... This is too confusing. I suppose if I was better at math it might seem like a better teaser... So good job!!
Woohoo!!! Got it without the hint!
The explanation is: 1*1 is always 1. Therfore the cube is 1, as it will always be 1, no matter to what power. And, as far as division 1/1 is always 1 so all the divisors are 1. Does that explanation help?
The explanation is: 1*1 is always 1. Therfore the cube is 1, as it will always be 1, no matter to what power. And, as far as division 1/1 is always 1 so all the divisors are 1. Does that explanation help?
^ a little bit, thanks...
n is a letter
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