M4apt

A Remainder is the portion is left unused after doing some process,In this context remainder is a number which is left when a number is divided by another number. In the basic levels of our education,we learn how to find remainders of normal maths expressions like Remainder("5",4)=1 but what if the question is asked in the form of Remainder( "19*19*17*21*9" ,"5") calculation part requires more time than the time we get to solve the same in the exam if we follow traditional methods. Divisor A number by which another number to be divided.

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 ...