SOLUTION: what is the three digit number that can be made from the digits 2, 3, 5 and 7 where no two digits in the three digit number are alike and where the three digit number is a multiple

Question 697666: what is the three digit number that can be made from the digits 2, 3, 5 and 7 where no two digits in the three digit number are alike and where the three digit number is a multiple of each of the digits chosen?
Answer by Positive_EV(69) (Show Source): You can put this solution on YOUR website!
Any number divisible by two must be even, and any number divisible by five must end in a zero or five. Therefore, if you use the two or the five, it must be the last digit, or else the resulting number will not be divisible by that number. Therefore, only one of the two or five can be used, and it must be the last digit -- meaning the 3 and the 7 must be used.

This means there are only four possible combinations: 372, 375, 732, and 735. For a number to be divisible by 3, the sums of the digits must be divisible by 3. All of these numbers satisfy this requirement, so all four numbers are divisible by 3.

There's no super-easy test for divisibility by 7, so you'll just have to divide the numbers by seven by hand to see which is correct. Dividing the numbers by seven shows that 735/7 = 105 is the only number of the lot divisible by 7, so the number is 735.
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