240 is the smallest number with at least 19 factors. 240 has twenty factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
262144 is the smallest number with EXACTLY 19 factors
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19 is a prime number, so, the factors of 19 are 1 and 19.
The smallest prime factors are 2,3,5,7 thus the smallest number would be the product of these will be 210
240 is the smallest number with twenty factors.
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