SOLUTION: If n and p are different positive prime numbers, which of the integers n^4, p^3 and np has (have) exactly 4 positive divisors? (A) n^4 only (B) p^3 only (C) np only (D) n^4 a

Question 340307: If n and p are different positive prime numbers, which of the integers n^4, p^3 and np has (have) exactly 4 positive divisors?
(A) n^4 only
(B) p^3 only
(C) np only
(D) n^4 and np
(E) p^3 and np

Could you please explain the above problem.
Answer by AnlytcPhil(1807) (Show Source): You can put this solution on YOUR website!
If n and p are different positive prime numbers, which of the integers n^4, p^3 and np has (have) exactly 4 positive divisors?



n⁴ = nnnn has divisiors 1,n,nn,nnn,nnnn that's 5

p³ = ppp has divisors 1,p,pp,ppp, that's 4

np has divisors 1,n,p,np, that's 4



So the answer is



(E) p³ and np



Edwin 

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