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Offhand, I would say that it is 48.

1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 all divide into 48.

I'm sure I can't think of any smaller numbers with that characteristic.

Supplement:

That is correct.

Factorise 10 = 5*2

Reduce each factor by 1 to give 4 and 1

The required number is 24*31 = 16*3 = 48

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Q: What is the smallest positive number with ten positive integer divisors?
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