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The required number is 90. The values produced by dividing 90 by 2, 3, 5, 7, and 11, the five smallest prime numbers, do not satisfy all the requirements: 90/2 = 45, which is not evenly divisible by 2; 90/3 = 30, which is not evenly divisible by 9; 90/5 = 18, which is not evenly divisible by 5; and the quotient of 90 and either 7 or 11 is not an integer itself.

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