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Remainders in math expressions

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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.

Units place in math expression

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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