Latest TCS Aptitude Question SOLUTION: find the last digit of 322^369

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(#M40040713) TCS Category question Keep an EYE

find the last digit of 322^369

Asked In TCS Puja (9 years ago)

Solved BHASKAR MANDAL Read Solution (14)

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BHASKAR MANDAL  (9 years ago) Best Solution

for calculating the unit place of these type of question (exponent)
as the power of 2 repeats after 4, so we will divide the exponent by 4
e.g, 2^1 = 2 and 2^(4+1) = 32, both have same unit place

369/4 gives the remainder as 1
so we can write 322^369 = 2^1 = 2
so, the unit place will be 2

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sharad  (9 years ago)

369 %4=2
so ans is 4

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Puja   (9 years ago)

i m confuse in 2 or 4.
322*((322)^4)92
focus on the last digit ___2
since((322)^4)^92=(2^4)^92
since the cyclicity of 2 is 4
so this no will produce last digit=2
so the no. ((322)^4)^92=___2 as last digit * 322=___4 as last digit.

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BHASKAR MANDAL  (9 years ago)

puja my procedure is correct , just take the remainder of the power and write it (remainder) as the power of the unit digit.
here remainder is 1, and the unit digit in the base is 2
so 2^1 = 2 will be the unit digit.

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awanish  (9 years ago)

2 as 2^9 is 2

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Archana Singh  (9 years ago)

For finding the unit digit of any number ignore the digits upto tens place and only take last digit as the valid number,then divide its power by 4.Its remainder will give you the result and if it gives remainder 0,then consider the power as 4.Here,Divide the power of 2 by 4 and the remainder will give you the unit place.In this case,369/4=1,so 2^1=2.
So answer is 2.

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Utkarsh Kumar Singh  (9 years ago)

it should be 8 because 369 is of form 4n+3 so 2*2*2=8

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DEBARSHI BISWAS  (9 years ago)

The power is 369.
According to rule First We have to divide the last two digits of the power means 69 By 4.
Here We get 1 as remainder.
So The Unit Place will Be 2^1=2.

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Saurabh Mishra  (9 years ago)

2
4
8
6 repeated unit digits.
so 369/4 remainder=1
so unit digit is 2

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Saptadipa Ghosh  (9 years ago)

if we take unit digit ie 2 from 322 and 9 from 369 and apply the operation 2^9=512
so from above operation it is clear that unit digit of 322^369= 2

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Utkarsh Kumar Singh  (9 years ago)

rectifying my answer 369 is of form 4n+1 so remainder is 2

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Utkarsh Kumar Singh  (9 years ago)

rectying my answer 369 is of form 4n+1 so the unit digit is 2.

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Suvisha Gupta  (9 years ago)

To find the units place we r only concerned with the last two digits of the power and instead of taking 322 we will take 2 so , 322^369 =2^69
2^69=(2^4)^17 * 2
Now the remainder of (2^4)^17 = 6
So , 6*2=12
Hence the unit digit comes out to be 2.
Ans = 2

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Abhijit Das  (9 years ago)

322^369
ENDING NO. 2 AND 369 IS FORM OF (4*N +2)
SO, FROM THE RULES OF UNIT DIGIT ANS IS 2

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