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A positive integer is called terrific if it has exactly 5 positive divisors.   What is the smallest terrific positive integer?

 Jun 23, 2024
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A terrific number must be a perfect square since it has an odd number of divisors. 

It also has 1 set of divisors other than 1 and itself. 

\(1,4,9\) all don't work since they only have 3 divisors. 

 

However, \(16\) has exactly 5 factors. We have \(1,2,4,8,16\)

 

Thus, our answer is 16. 

 

Thanks! :)

 Jun 23, 2024

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