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6 in any integer power >0 has the last digit 6. Integer ending with 6 divided by 2 can have 3 or 8 as last digit. But as 6^8 will be divisible by 4 for sure, divided by 2 it must give the even number, hence 8 is the correct answer.

Another solution: \frac{6^8}{2}=\frac{2^8*3^8}{2}=2^7*3^8

Cyclisity of both 2 and 3 is 4, hence 2^7 has the same last digit as 2^3=8 and 3^8 has the same last digit as 3^4=81, hence 8*1=8.

I used first approach, took me 11 secs , so maybe there is a shortcut?
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Re: What is the last digit of 6^8/2 ? [#permalink]
18 Feb 2014, 00:47

6 multiplied by 6 any times would give the last digit 6 itself However 6 multiplied by 3 would give 8 in the last place. So has been factorized accordingly
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Re: What is the last digit of 6^8/2 ? [#permalink]
05 Mar 2014, 22:30

Is there a reason we don't have any possible options to choose from in the original post?

How my brain processed this:

Step 1 --> 6^(Any Power) will end in a 6 (i.e. 6*6 = 36, 6*6*6 = 216, etc.). To me this makes sense to do first based off order of operations. Step 2 --> Take any result an divide by 2. Quick and easy would be 36/2 = 18. Any answer will be 8!

Where you can trip yourself up is assuming you take 6/2=3, and to me if you stick to order of operations you can avoid this mistake.