Easy Way to Calculate Remainder of Long Division

       Most of the calculators unable to calulate Remainder of long division.
Today I am going to show you a easy way to Calculate Remainder of Long Division using square-and-multiply algorithm.

Consider example as (25)¹⁷ % 77

As we know,
            25¹⁷ = 25¹⁶ x 25¹
So we perform steps as follows:
            25¹ % 77 = 25
            25² % 77 = 9
            25⁴ % 77 = 9² % 77 = 4
            25⁸ % 77 = 4² % 77 = 16
            25¹⁶ % 77 = 16² % 77 =25

Since, 17 = 16 + 1 we stopped after 25¹⁶ % 77

 Final computation,
            (25)¹⁷ % 77 = { [ (25)¹⁶ % 77 ] x [ (25)¹ % 77 ] } % 77
                                = { 25x25 } % 77
                                = 9


 Happy Coding With Mathematics!