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Is there a way of filling a $4\times4$ table with $16$ distinct integers from $1,2,\ldots,100$ such that the products of the numbers in every row and in every column are all equal to each other?

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The largest prime number that could be in the table is 23. – Tony Ruth Feb 27 at 18:35
up vote 15 down vote accepted

Notice that each row and each column contains the numbers 1, 1, 2, 3, 4, 5, 6, 7

$$ \begin{array}{ a b c d } 4*7 & 1*6 & 3*1 & 2*5 & \\ 3*5 & 2*1 & 4*6 & 1*7 &\\ 1*1 & 4*5 & 2*7 & 3*6 &\\ 2*6 & 3*7 & 1*5 & 4*1 &\\ \end{array} $$

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