A multiplicative magic square (MMS) is a square array of positive integers in which the product of each row, column, and long diagonal is the same. The $16$ positive factors of $2010$ can be formed into a $4\times 4$ MMS. What is the common product of every row, column, and diagonal? Write your answer in the corresponding blank on the answer sheet
The answer: That product raised to the 4th power should equal the product of the sixteen factors of $2010$. Note that $2010= (2)(3)(5)(67)$. Among the $16$ numbers, half of them have a factor of $2$ with multiplicity $1$ while the rest don’t have the factor $2$. Likewise, half of the 16 numbers have a factor of $3$ with multiplicity $1$ while the rest don’t have the factor $3$. The same holds for $5$ and for $67$. I don't get why the product is to the $4$th power ??? And why it is equal to the $16$ factors ?? I DO get the part about the factors .. $8$ of them will have factor of $2$ etc. ..