May 7th, 2015, 02:14 PM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  Last digit
find the last digit of 2^2009 
May 7th, 2015, 02:53 PM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361 
2

May 7th, 2015, 05:43 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,495 Thanks: 578 
$\displaystyle 2^5\equiv 2\pmod{10}$ $\displaystyle 2009\equiv 1 \pmod 4 $ 
May 8th, 2015, 04:40 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,097 Thanks: 847 
Did you try at all? An obvious first step would be to look at powers of 2 to see there were any pattern. 2^1= 2: last digit 2 2^2= 4: last digit 4 2^3= 8: last digit 8 2^4= 16: last digit 6 2^5= 32: last digit 2 2^6= 64: last digit 4 2^7= 128: last digit 8 2^8= 256: last digit 6 2^9= 512: last digit 2 2^10= 1024: last digit 4 2^11= 2048: last digit 8 2^12= 4096: last digit 6 Does that give you any ideas? 
May 8th, 2015, 01:30 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,495 Thanks: 578  
May 8th, 2015, 06:58 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,844 Thanks: 1566 
As $2^{2008} = 16^{502}$ has last digit 6, $2^{2009}$ has last digit 2.


Tags 
digit 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How many three digit number whose digit sum is 13 leave reminder 1 divided by 4  Shen  Elementary Math  3  June 6th, 2014 12:27 AM 
the last digit  shunya  Algebra  2  October 8th, 2013 05:03 AM 
the last nonzero digit of 13!  Albert.Teng  Algebra  3  October 6th, 2012 07:37 AM 
sum of digit  panky  Algebra  0  January 16th, 2012 05:48 PM 
no. of digit  panky  Algebra  3  December 13th, 2011 08:45 AM 