What is the 7 digit number if no two digits are the same and each number's digits divides into the number exactly. The seven digits are chosen from the numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. What is the mystery seven digit number?

9867312

9678312

Step-by-step explanation:

We followed the rule of division. For 7, the rule is:

Take the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7, then the number has 7 as a factor.

We assume our digits as 9, 8, 7, 6, 3, 2, 1.

To be divisible by 8 (and by 4 and 2 as well), the last three

digits must be a multiple of 8. We want to use the smallest numbers

there; 312 will work and we have:

9 _ _ _ 3 1 2

We are left with three numbers 8,7,6 which can be arranged in 6 ways.

The six possible arrangements are:

876, 867, 678, 687, 768, 786.

From the above arrangements, only two fixed into the missing number:

867 and 678.

Hence we have the numbers;

9867312

9678312