Asked by Anonymous
Find the last two digits of the number 11^2016 .
I need to figure out how to hand do this and show all my work. Help pls
I need to figure out how to hand do this and show all my work. Help pls
Answers
Answered by
Steve
Start a table of the powers of 11
n 11^n
1 11
2 121
3 1331
4 14641
The last 2 digits just cycle through
11
21
31
...
91
01
11
21
...
So, 11^2016 ends in 61
Or, you might find this article on modular arithmetic useful:
https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/fast-modular-exponentiation
n 11^n
1 11
2 121
3 1331
4 14641
The last 2 digits just cycle through
11
21
31
...
91
01
11
21
...
So, 11^2016 ends in 61
Or, you might find this article on modular arithmetic useful:
https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/fast-modular-exponentiation
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