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Director
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Please provide answer with solution
241. If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^2 have?
a 4
b.5
c.6
d.8
e.9
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Director
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Please provide explaination. Thanks
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Intern
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the number of divisors would be 5
the number has to be square of a prime number , for it to have 3 divisors.
the divisors for n ^ 2
1, root(n) , n , n^1.5 , n ^2
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VP
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I would just take a number with 3 divisors, say
n=4 (divisors: 1, 2, 4)
n^2=16 (divisors: 1, 2, 4, 8, 16), so 5 divisors!
also square of an integer has odd number of divisors, whereas even number of divisors tells us that such number doesn't have a square. Based on that it could not be A, C or D
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Director
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5 --- Suppose n = 9 then n sqre = 81
which has 1, 3, 9, 27, and 81 as divisor
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Manager
Joined: 11 Oct 2005
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I got 5 as well...pick a number with 3 divisors and square it
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