We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
147
2
avatar

How many positive integer divisors of 23,328 are perfect cubes?

 Dec 24, 2018
 #1
avatar+102461 
+2

How many positive integer divisors of 23,328 are perfect cubes?

 

23328^(1/3) = 28.573218935427587   Well less than 29 anyway.

 

1 is ok

factor(23328) = 2^5*3^6

 

 

\(2*2*2*2*2\quad * \quad 3*3*3*3*3*3\\~\\ 1^3,2^3,3^3,6^3,9^3,18^3 \;\;\text{that seems to be it.} \)

 

I just got those from visual examination of the factors.

So that is  6 of them.

 Dec 24, 2018
 #2
avatar
+1

23,328 = 2^5 * 3^6

Will divide the exponents by 3 and add 1 and then multiply them:

5 /3 + 1 =2

6/3  + 1 =3

So, 3 x 2  = 6 perfect cubes.

 Dec 24, 2018

7 Online Users