We can check that a number is divisible by 7 or not by following method
Start at the right digit, and go left. 1st digit + 3 times the 2nd digit + 2 times the 3rd digit  the 4th digit  3 times the 5th digit  2 times the 6th digit. And then we repeat the sequence, + the 7th digit + 3 times the 8th digit and so on .
If the whole "sum" is divisible by 7, then the original number is divisible by 7.
Example :
85627878
8+3(7)+2(8)73(2)2(6)+5+3(8) = 49
since 49 is divisible by 7 therefore 85627878 is also divisible by 7.
This is a good and fast method.
