150.
100/ 6 = 16 2/3 so 17 x 6 = 102 is the first three digit multiple of 6
1000 / 6 = 166 2/3 so 166 x 6 = 996 is the last three digit multiple of 6
So there are 166 - 17 + 1 = 150 three digit multiples of 6.
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Three of them.
To find the number of three-digit positive integers with digits whose product is 24, we can break down 24 into its prime factors: 2 x 2 x 2 x 3. The possible combinations for the three digits are (2, 2, 6), (2, 3, 4), and (2, 4, 3). These can be arranged in 3! ways each, giving a total of 3 x 3! = 18 three-digit positive integers.
31 + 62 + 93 + 13 + 26 + 39 = 264
There are 720 of them.
17