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Intern
Joined: 17 Apr 2010
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Hi everybody! I got a question concerning the pattern of getting the units digit in questions like the following: What is the units digit of 3^17 × 17^54 × 135^19 × 31^21 × 42^17? Is it true that the units digit is repeated with every 4th power, i.e. 3^2 has the same units digit as 3^6 and 3^10? My approach: 3^17 ---> 17 divided by 4, remainder 1---> 3^1 ---> Units digit 3 17^54 ---> 54 divided by 4, remainder 2---> 7^2 ---> Units digit 9 135^19 ---> 19 divided by 4, remainder 3---> 5^3 ---> Units digit 5 31^21 ---> 21 divided by 4, remainder 1---> 1^1 ---> Units digit 1 42^17 ---> 17 divided by 4, remainder 1---> 2^1 ---> Units digit 2 3 x 9 x 5 x 1 x 2 = 270 Answer: Units digit = 0. Would this be a good approach?
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VP
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CEO
Joined: 17 Nov 2007
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Your approach is good. 1,1,1,1, 12,4,8,6, 23,9,7,1, 34,6,4,6, 45,5,5,5, 56,6,6,6, 67,9,3,1, 78,4,2,6, 89,1,9,1, 90,0,0,0, 0You can also use that: 1,5,6,0 is repeated with every 1st power (You can ignore power) 4,9 is repeated with every 2nd power (odd|even power = 1st|2nd power)
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Intern
Joined: 17 Apr 2010
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thx for your answers!
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Manager
Joined: 06 Apr 2010
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As I understand it, whenever there is a product of multiple of 5's and multiple of 2's , we will always end up with a last digit of zero's. Example: 5 ^1* 2^1 => last digit is 0 5^2 * 2^2 => last 2 digits are 0 so 5^19 * 2^17 will have 17 0's on the right hand side. Someone please correct me if I'm wrong... 
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CEO
Joined: 17 Nov 2007
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Eden, you are right.
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Manager
Joined: 08 Oct 2010
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Pls. find everybody very useful the reference of hussain15 to the link http://takshzilabeta.com/index.php?opti ... -&Itemid=5 Thank you very much Hussain!!!
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Intern
Joined: 09 Feb 2012
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Hi all,
i was just wondering if it is always possible to use the approach of "intern" with those kind of questions?
It seems the most easiest way to me.
Many thanks
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