Minimum Deletions

The *greatest common divisor* (GCD) of a sequence is the greatest positive integer which divides each element of this sequence. You are given a sequence $A$ of positive integers with size $N$. You are allowed to delete up to $N-1$ elements from this sequence. (I.e., you may delete any number of elements, including zero, as long as the resulting sequence is non-empty.) Please find the minimu