+0  
 
0
22
1
avatar

How many positive perfect cube factors does \(3^55^{10}\) have?

 

So what I'm doing right now is checking with a calculator whether a divisor is a perfect cube...Is there a faster way to do this? (btw, I know it is a repost but the answer for that question was incorrect.)

Guest Oct 31, 2018
 #1
avatar
+1

You calculate perfect cubes as follows:

Take the exponent / 3 (use integer part only) + 1 = 5/3 + 1 =2, and 10/3 + 1 = 4. Then multiply them together:

So, 2 x 4 = 8 perfect Cubes in 3^5 x 5^10 as follows: (1^3, 3^3, 5^3, 15^3, 25^3, 75^3, 125^3, 375^3) =8

P.S. These Perfect Cubes are divisors(factors) of 3^5 * 5^10.
 

Guest Oct 31, 2018
edited by Guest  Oct 31, 2018

29 Online Users

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.