Find the smallest positive integer multiple of 84 whose base ten representation uses only the two digits 6 and 7.

84=3*4*7

1, To make the number dvisible by 4 it must end by  76.

2. The digits before 76 must sum up to a result being 2 mod 3, at  least 2 sevens and 1 three, making a total divisible by3,so 67776, 76776 and 77676 are divisible by 12,

3. Only 76776 is divisible by 7 (776-76=700) therefore

76776 is the  smallest positive integer multiple of 84

Posted by Ady TZIDON on 2014-08-02 14:44:58