# The last digit of the number (373)³³³ will be?[373 to the power 333]

1
by Srushti13

2014-05-23T10:00:21+05:30

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There is a shortcut method to solve such problems
Suppose x is raised to the power y and we need to find unit digit of .
So, we will first divide y by 4 and find the remainder thus obtained. Since on dividing and integral number by four can yield only four remainders --> 0, 1, 2 and 3.
This method applies for 4 values of x only, because for other values, you can split the values in the 4 values of x:-
x = 2, 3, 7 and 8.
For 2
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If remainder [y/4] is 1, unit digit of  = 2
If remainder is 2, unit digit of  = 4
If remainder is 3, unit digit of  = 8
If remainder is 0, unit digit of  = 6

For 3
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If remainder is 1, unit digit of  = 3
If remainder is 2, unit digit of  = 9
If remainder is 3, unit digit of  = 7
If remainder is 0, unit digit of  = 1

For 7
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If remainder is 1, unit digit of  = 7
If remainder is 2, unit digit of  = 9
If remainder is 3, unit digit of  = 3
If remainder is 0, unit digit of  = 1

For 8
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If remainder is 1, unit digit of  = 8
If remainder is 2, unit digit of  = 4
If remainder is 3, unit digit of  = 2
If remainder is 4, unit digit of  = 6

For memorising that of 3 and 7, you can check the unit digit of when 3 and 7 are raised to the power remainder [power = remainder]. For 2 and 8 this trend doesn't works.