+500 The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
We know that we can't have a two digit factor in one of our three digit numbers(it can't fill in one digit), so we are left with:
1,2,3,4,6,8
Now, we can just bash out unique cases:
138
146
226
234
These are all the unique cases, for which you can reverse these to form any other arrangements that work(do you see the way I wrote it out systematically?) Notice that I write these numbers such that they're in ascending order, with the digits of each 3 digit number going in ascending order(in other words, the digit on the right of a given spot is either equal or greater in value than that digit). We now multiply out the number of ways we can arrange these to get our final answer.
138 = 3! = 6 ways
146 = 3! = 6 ways
226 = 3!/2! = 3 ways
234 = 3! = 6 ways
add all these up, and we get:
6+6+3+6 = 21 numbers, meaning our answer is E)
