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Let n be an odd integer with exactly 11 positive divisors. Find the number of positive divisors of \(8n^3\).

 

Thanks for any help.

 Apr 5, 2022
 #1
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8n^3 has 34 divisors.

 Apr 5, 2022
 #2
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n==3^10 ==59,049 ==(1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049)>>Total = 11 divisors.

 

8 * 59049^3 ==1,647,129,056,757,192==2^3  x  3^30

 

Number of divisors==[3 +1]  x  [30 + 1] ==4  x  31 ==124 divisors.

 Apr 5, 2022
 #3
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124 is correct. Thanks!

SpaceXGeek  Apr 5, 2022

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