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UKMT Junior Mathematical Challenge, 2023

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

The positive integers from 1 to 9 inclusive are placed in the grid, one to a cell, so that the product of the three numbers in each row or column is as shown. The grid is $3\times3$ . The row products (top to bottom) are $18$ , $105$ , $192$ . The column products (left to right) are $56$ , $180$ , $36$ . What number should be placed in the bottom right-hand cell?

(A) $9$ (B) $6$ (C) $4$ (D) $3$ (E) $2$

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