Latest A website Aptitude Question SOLUTION: find the remainder when 2^2014 is divided by 10

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find the remainder when 2^2014 is divided by 10

Asked In A website Harsh Poddar (10 years ago)

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Saraswathy  (10 years ago)

2^1 % 10 = 2
2^2 % 10 => 4%10 = 4
2^3 % 10 => 8%10 = 8
2^4 % 10 => 16%10 = 6
2^5 % 10 => 32%10 = 2
2^6 % 10 => 64%10 = 4
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The cycle is upto the power of 4... Again it goes on like 2, 4, 8, 6,..

We can write 2014 as --> 4*503+2 [since 4*503=2012... cycle is upto 4th power... so i multiplied with 4...]
So upto 2012, 503 cycles got over...
Again next cycle starts with the remainder of 2...
For the power 2013, remainder=2
For the power 2014, remainder=4

Ans : 4

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ABHOY KUMAR  (10 years ago)

[REMAINDER = 4]
Any no. divided by 10 gives the unit digit of that no. as a remainder.
here,for 2^n expression ,unit digit is repeated every after 4 cycle..
so, 2^2014 has unit digit = 2014/4=2;unit digit will be 2^2= 4.
so, remainder will be 4

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rajasekar  (10 years ago)

2^1 % 10 = 2
2^2 % 10 => 4%10 = 4
2^3 % 10 => 8%10 = 8
2^4 % 10 => 16%10 = 6
2^5 % 10 => 32%10 = 2
2^6 % 10 => 64%10 = 4
2014%4==2
2^2=4

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