The number N is a multiple of 7. The base 2 representation

[Mellie]

The number N is a multiple of 7. The base 2 representation of N is
[10110101010101ABC110.]
Compute the ordered triple of digits (A,B,C).

[Guest]

In base 10 a number is divisible by 9 if and only if its digits add up to something which is divisible by 9
The same trick works in base 8 for divisibility by 7.
It is easy to convert a base 2 number to base 8, just group the binary digits into groups of 3, so the number in question in base 8 is:
26525?6
The known octal digits add up to 26 (in base 10) so for this to be a multiple of 7 the unknown digit must be 2.
So A,B,C are 0,1,0 respectively,

Hope this helped,

R. Baber.