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Given that \(n > 1\), what is the smallest positive integer \(n\) whose positive divisors have a product of \(n^6\)?

 Jan 1, 2019

Best Answer 

 #1
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N=60
1 | 2 | 3 | 4 | 5 | 6 | 10 | 12 | 15 | 20 | 30 | 60 (12 divisors)
60 x 30 x 20 x 15 x 12 x 10 x 6 x 5 x 4 x 3 x 2 x 1 =46,656,000,000
                                                                       60^6=46,656,000,000

 Jan 1, 2019
 #1
avatar
+1
Best Answer

N=60
1 | 2 | 3 | 4 | 5 | 6 | 10 | 12 | 15 | 20 | 30 | 60 (12 divisors)
60 x 30 x 20 x 15 x 12 x 10 x 6 x 5 x 4 x 3 x 2 x 1 =46,656,000,000
                                                                       60^6=46,656,000,000

Guest Jan 1, 2019

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