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The unit digit in the sum 26 4 102 + 26 4 103 264^{102} + 264^{103} is

8 6 4 0

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3 solutions

Kunal Gawade
Dec 31, 2014

so now we have to fing unit place digit of this two digit and and addition of this two digit then we have to take only unit digit of tha no tha t would be 264^102 so we have to find only 264^2 because we have to find only unit digit of that no and same for the other no 264^3

E x p . = 26 4 102 ( 1 + 264 ) = 26 4 102 265. S i n c e 26 4 102 i s e v e n a n d u n i t d i g i t o f 265 i s 5 , t h e i r p r o d u c t w i l l h a v e 0 a s i t s u n i t d i g i t . Exp. =264^{102}*(1+264)=264^{102}*265.~~~\\Since ~264^{102}~ is ~even~and~unit ~digit~ of 265~is~5,~\\ their ~product~ will~have~ \boxed{0} ~as~its~unit~digit. \\
Note :-An even integer raised to any positive integer, results into an even number.

264 i s e v e n . 26 4 102 , r e s u l t i s e v e n . 264 ~ is ~ even. ~ 264^{102} ~,result~is ~even.

Vishal S
Dec 17, 2014

Since the unit digit of even power of 4 is always 6 and odd power is 4

therefore the unit digit of 264^102+264^103 is 6+4=10=>0

A nice way of thinking. Congratulations.

Niranjan Khanderia - 6 years, 5 months ago

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