So Many 2's

Find the last digit of the following: 2 44444444444444 {2}^{44444444444444}

0 4 2 6 8

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1 solution

Brian Wang
Nov 20, 2015

2 1 {2}^{1} = 2
2 2 {2}^{2} = 4
2 3 {2}^{3} = 8
2 4 {2}^{4} = 16
2 5 {2}^{5} = 32
The last digits go 2,4,8,6,2,.....
444444444444444 is divisible by 4.
Because the repeating group is 4 numbers long, the last digit is 6.

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