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An infinite number.

Start with 1*1*24, 1*2*12, 1*3*8, 1*4*6

then 2*2*6, 2*3*4

Then try some fractions:

0.1*0.1*2400, 0.1*0.2*1200, etc

and then there are irrationals.

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Q: How many different boxes can you make with volume of 24 cm?
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