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)-7-3(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.