21^100 - Last Two DigitsDate: 09/04/97 at 21:19:52 From: K Subject: 21^100 What are the last two digits of 21 to the 100th power? Date: 09/05/97 at 07:32:48 From: Doctor Anthony Subject: Re: 21^100 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 -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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