+0  
 
0
55
2
avatar+398 

How many factors of \(2^5\cdot3^6\) are perfect squares?

RektTheNoob  Sep 27, 2018
 #1
avatar+2319 
+2

Any product made up of pairs of like prime factors will be a perfect square

 

there are 2 unique pairs, (2,2), (3,3)

 

there are 3 unique tetrads (2,2,2,2), (2,2,3,3), (3,3,3,3)

 

there are 3 unique hexads (2,2,2,2,3,3), (2,2,3,3,3,3), (3,3,3,3,3,3)

 

there are 2 unique octads (2,2,2,2,3,3,3,3), (2,2,3,3,3,3,3,3)

 

there is 1 unique decad (2,2,2,2,3,3,3,3,3,3)

 

So 11 perfect square factors 1, 4, 9, 16, 36, 81, 144, 324, 729, 1296, 2916, 11664

Rom  Sep 27, 2018
 #2
avatar
+1

Number of perfect squares in: 2^5 x 3^6 =
2^0, 2^2, 2^4=3
3^0, 3^2, 3^4, 3^6=4. Therefore the number of perfect squares that are factors of: 2^5 x 3^6= 3 x 4  =12 

Note: Rom made a small typo by not adding 1 to the total of 11, even though he listed it.

Guest Sep 27, 2018
edited by Guest  Sep 27, 2018

34 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.