If 2016*N is a perfect square then what is the smallest positive integer Value for N

Question

 Note that 2016 = 2⁵ X 3² X 7

Answer 1

Hi Shakya,

 

The first thing you want to do is write 2016 as its prime factorization: 2016 = 2⁵*3²*7. The 3² is already a square. We need too multiply one more factor of 2 to make 2⁶, which has 2³ = 8 as its square root. We also need to multiply by 7 to give 7². Therefore, to make a perfect square out of 2016, we need to multiply by 2*7 = 14. So, N  =14.