A delivery service can consider shipping boxes with weights which are factors of 18. A total of 12 pounds of material needs to be shipped. If all of the boxes weigh the same, calculate the maximum possible weight in pounds for each box.

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Solution

Factors of 18 are 1, 2, 3, 6, 9, 18.
$\Rightarrow$ Each box can weigh 1 pound, 2 pounds, 3 pounds, 6 pounds, 9 pounds or 18 pounds.

Factors of 12 are 1, 2, 3, 6, 12.
$\Rightarrow$ Each box may have 1 pound, 2 pounds, 3 pounds, 6 pounds, or 12 pounds of material if all the boxes weigh the same.

Hence, the maximum possible weight of each box which is also a factor of 18 is 6 pounds.

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