M4apt

Many exams try to make you feel that you cannot solve the problem by making question as big as possible like units place of (186937)^178909 but solving this problem is as simple as solving 9%4 Before solving these kind of problems, understand the great concept called Cyclicity of numbers which states that any digit when multiplied by itself repeatedly, generates a cycle of digits. points to remember: Only units place will be responsible for generating units place Every number after applying successive multiplications,repeats the cycle of digits. So try to figure out a common series in powers of digits for example units(3)=3,units(3*3)=9,units(9*3)=7,units(7*3)=1,units(1*3)=3(we get a cycle of multiplication) Number      powers                         Series/cycle(units place of powers column) [cyclicity of number] 2                 2,4,8,16,32                   2,4,8,6                    [4] 3                 3,9,27,81,243               3,9,7,1