Question

last two digits of 21^100​

Answer 1

The last two digits follow a pattern:

     

    Number        Last two digits

      21               21

      21^2             41

      21^3             61

      21^4             81

      21^5             01

      21^6             21

      21^7             41

and so on.  

The last digit is always 1, and the second to last goes through the

sequence

 2, 4, 6, 8, 0,    2, 4, 6, 8, 0,  

So every 5th power gives the same final two digits.

Powers of 5, 10, 15, ......, 90, 95, 100  will all have 01 as the

final two digits.

The last two digits of 21^100  are  01

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