7. The positive integer $N$ has exactly six distinct (positive) factors including 1 and $N$. The product of five of these is 6075 . What is the value of the sixth factor?
SOLUTION
015

We determine that $6075=3^{5} \times 5^{2}$. This means that $1,3,5$ and 15 must be factors of $N$. Since $3^{5}$ is a factor of 6075,9 is also a factor of $N$ and so is $9 \times 5=45$. $1 \times 3 \times 5 \times 9 \times 15 \times 45=3^{6} \times 5^{3}$. Therefore, the missing factor is $3^{6} \times 5^{3} \div\left(3^{5} \times 5^{2}\right)=15$.