7777.... (80 digits) / 74 find the remainder
is dividing it and finding the pattern only option to find it?

3

Hi Shweta,

That's the best way to solve this problem.

7777 mod 74 is 7
So, one 7 is carried over as remainder for the first four 7s. After that, one 7 is carried over as remainder for every three 7s (because of the carried over 7 acting as the fourth 7)
78 is a multiple of 3
So, there will be one carry-over 7 after the first seventy-nine 7s.
So, the expression becomes 77 mod 74 = 3