In number theory, Co-prime numbers are those numbers if the only positive factor that divides them is \\\\(1\\\\).Here,Option A: \\\\((17,15)\\\\) Factor that divides both of them is \\\\(1\\\\).Option B: \\\\((10,16)\\\\) Factors that divides both oh them are \\\\(1,2.\\\\)Option C: \\\\((20,24)\\\\) Factors that divide both of them are \\\\( 1,2,4.\\\\)Option C: \\\\((31,62)\\\\) Factors that divide both oh them are \\\\(1,31.\\\\)In reference to above definition \\\\((17,15)\\\\) are co-prime numbers.Hence Option A is correct.