I think its a E. May be I am reading too much into it.
A - Not suff (K could be 16 or 8)
B - K= Eg.: 2^a X 3^b X 5^c X 7 ^d
If a=b=c=d=1, then K is exactly divisble by 4 diff prime numbers. K cannot be a square
But a=b=c=d=2 then K is still divisible by 4 diff prime numbers. K can be a square in this case
Hence B not suff
C - not suff as well a=2, but doesn't say much abt b, c, and d