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110
30
10
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 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