Pre-Calculus Help Please!?

Question

The number N is a multiple of 7. If the base 2 representation of N is 1 0 1 1 0 1 0 1 0 1 0 1 0 1 A B C 1 1 0 compute the ordered triple of digits (A, B, C)

Answer 1

Probably easier doing with  base 8  number:

26526x6 base 8  where x = ABC base 2

in Base 8,  multiple of 7 are 7,16,25,34,43,62 61.

if you do the actual division, we get x=2 base 8.

which is 010 bas 2.

(A,B,C) is  (0,1,0 )

Of course, you can also do it with binaries.