# When 2 to the power of 2015 is completely calculated the units place of number obtained is?

1
by vghfghf

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by vghfghf

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2 power1 = 2 (units digit is 2 )

2 power 2 = 4 (units digit is 4 ) and so on

2 power 2 has units digit 4

2 power 3 has units digit 8

2 power 4 has units digit 6

2 power 6 has units digit 4

here we can see it repeats for every 4 times

whenever n is multiple of 4 the unts digit of 2 power n is 2

that is

2 power 4 has units digit 2

2 power 8 has units digit 2 ...etc

As 2012 is multiple of 4

at this point we can find the units digit of 2 power 2012 is 2

units digit of 2 power 2013 is 4

unit digit of 2 power 2014 is 8

and units digit of 2 power 2015 is 6

therefore units place of 2 power 2015 = 6