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A positive divisor d of \(N = 2^4 \cdot 3^6 \cdot 5^8\) is chosen uniformly at random. What is the probability that d is a perfect cube?

 Feb 22, 2020
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Your N = 315 divisors, 18 of which are Perfect Cubes:

 

So, the probability is: 18 / 315 = 2 / 35

 Feb 22, 2020

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