If q and r are prime numbers and n=4qr, which of

If q and r are prime numbers and n=4qr, which of the follwing could be the number of factors of n that are between 1 and n?


(I) 3
(II) 4
(III) 7










Case 1:
q does not equal r and neither one equals 2.
n= 2^2*q*r; number of factors (excluding n and 1) = 3*2*2-2=10

Case 2:
q does not equal r and one of them equals 2.
n=2^3*r; number of factors (excluding n and 1) = 4*2-2=6

Case 3:
q=r but does not equal 2.
n=2^2*q^2; number of factors (excluding n and 1) = 3*3-2=7

Case 4:
q=r=2
n=2^4; number of factors (excluding n and 1) = 5-2=3

Answer is C.