There are at least 2 necklaces. On each necklace there is the same number of diamonds, on each at least 2. If we knew the number of all diamonds, we would also know the number of necklaces. The number of all diamonds is bigger than 200 and smaller than 300. How many necklaces is there?

(A) 16

(B) 17

(C) 19

(D) 25

(E) Some other number