South African Mathematics Olympiad First Round

Factorise $2016$. It is divisible by $2$, because it is an even number and it is also divisible by $9$ since the sum of the digits is $9$. The full factorisation is $2^5\times 3^2\times 7$. Each prime factor of a complete square must have an even number as the exponent (i.e. every prime factor must appear an even number of times) so that $2016$ multiplied by a number $n$ will be a complete square. Therefore, $n$ must be equal to $2\times 7$ which is equal to $14$.