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What is the smallest number with exactly 14 divisors?

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Dozens

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Weekly Problem 25 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1
The square whose vertices are the centres of the original four circles has side of length 2 units and this distance is equal to the diameter of the circle through $X, Y, Z$ and $T$.

This problem is taken from the UKMT Mathematical Challenges.

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