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How about 6 whose factors are 1, 2, 3 and 6
2 and 3 are the smallest prime numbers. So answer is 2^3 * 3^3 = 216
The smallest prime number, of course, is 2. The smallest prime number whose digits add up to 2 is, of course, 2. The next-smallest is 11. It is left as an exercise for the reader to determine whether the other numbers whose digits add up to 2 (e.g. 101, 1001, 10001) are prime.
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I belive it is 4. The factors of 4 are 1,4, and 2.