TITLE: Constructing a seven digit number such that one divides the other
QUESTION [5 upvotes]: This was asked to me by a friend. I tried this problem for a long time, but i couldn't solve it. Seems interesting though. 
Prove that it is impossible to construct two different seven digit numbers, one of which is divisible by the other, out of the digits 1,2,3,4,5,6,7 (All seven digits must be in each number)

REPLY [2 votes]: 7654321/1234567 = 6. something 
so x = ky where 2<=k<=6
sum of the digits are not divisible by 3 so no 3 and 6.
now x = ky where k = 2,4 or 5 so not possible.