If integer n has exactly 3 positive factors, including 1 and

Question

If integer n has exactly 3 positive factors, including 1 and n, how many positive divisors does n^2 have?

a. 4
b. 5
c. 6
d. 8
e. 9

Please show your workings

FN · Answer

usually the square of a prime number has 3 factors..

so take 2^2=4 has 3 factors, so does 9 and 25 etc..

4^2=16...

factors are 1, 2, 4, 8, 16..

9^2=81 factors are 1, 3, 9, 27, 81
i.e 5 factors

brokerbevo · Answer

Since this is a problem solving question (not DS), we can just pick a number that satisfies the initial constraints and apply it to the question.

4 and 9 are two examples where there are exactly 3 factors including and 1 and n.
4 = 1, 2, 4
9 = 1, 3, 9

For 4^2 = 16 and the factors of 16 are 1, 2, 4, 8, and 16 --> total of 5 
For 9^2 = 81 and the factors of 81 are 1, 3, 9, 27, and 81 --> total of 5

Answer:  B

maratikus · Answer

n has exactly 3 positive factors -> n = p^2 -> n^2 = p^4 -> 5 factors -> B

FN · Answer

yeah..nice method just remember that P^N...where N+1= equal to number of factors..

Prep Toolkit