Latest TCS Aptitude Question SOLUTION: what is the remainder of (16937^30)/31 ?

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(#M40024512) TCS Logical Reasoning question Keep an EYE

what is the remainder of (16937^30)/31 ?

Asked In TCS GAURAV JAISWAL (10 years ago)

Unsolved Read Solution (19)

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Read Solution (19) :

sakshi sahni  (10 years ago)

(16937^30)/31
= ((16937%31)^30)%31 i.e (11^30)%31 (by remainder theorem)
= (121^15)%31
=(28^15)%31 =28(784^7)%31
=28(9^7)%31
=28*9*(19^3)%31
=1728468%31=1

Is this solution Helpfull? Yes (28) | No (1)  

sandy  (10 years ago)

@ JIGNESHKORADIYA
1 is the ans
(16937^30)/31=(15^30)/31(as 15 is the remainder when 16937 is divided by 31)
we can write (15^30)/31 as (225^15)/31
which is equal to (8^15)/31 (as 8 is the remainder when when 225 is divided by 31)
we can write 8^15/31 as (64^7*8/31) = (2^7*8/31) as 2 is remainder when 64 is divided by 31
we can write 2^7*8/31 as ((32*2^2)*8)/31 =(32*32)/31
which when divided by 31 leaves remainder (1*1)/31
so remainder is 1

Is this solution Helpfull? Yes (9) | No (11)  

Balakumaran  (10 years ago)

1 is the answer

Is this solution Helpfull? Yes (6) | No (1)  

Gudivada sunitha  (10 years ago)

answer is 1.consider last two digits 37^30/31= 7^30. odd power even is 1

Is this solution Helpfull? Yes (3) | No   

ravi kumar  (10 years ago)

by using fermats theorem u can directly get the ans 1.

Is this solution Helpfull? Yes (3) | No   

Deblina Manna  (10 years ago)

ravi kumar,will u pls tell me what is fermest theorem??

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Rohit Bohra  (10 years ago)

when we divide 16937 by 31 we got 15 as remainder
then we have now (15)^30 so make (15*15) groups of this will result in 15 group
now divide 225/31 we got remainder 8 of 15 times so make (8*8) groups this will result in 7 groups and one 8 extra
now divide 64%31=2
this 2^7 and 2^3= 2^10%31 we got final result 1

Is this solution Helpfull? Yes (2) | No (5)  

kalyani dangeti  (10 years ago)

16937%31=11
11^30=11^28*11^2
11^2=121%31=28
hence ans=28 % =remainder

Is this solution Helpfull? Yes (2) | No (2)  

twinkle goyal  (9 years ago)

ans is 1
[sakshi sahni]
(16937^30)/31
= ((16937%31)^30)%31 i.e (11^30)%31 (by remainder theorem)
= (121^15)%31
=(28^15)%31 =28(784^7)%31
=28(9^7)%31
=28*9*(19^3)%31
= 252%31 * 19^2%31
=14*20%31
=so remainder is 1

Is this solution Helpfull? Yes (2) | No   

Arshal Jain  (10 years ago)

i think 30 is the answer to the question

Is this solution Helpfull? Yes (1) | No (3)  

jigneshkoradiya  (10 years ago)

plz explian any oneeeeeeee

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Fighter  (10 years ago)

1 is the answer

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silvia joyce.B  (10 years ago)

using remainder theorem ans is 1

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Pratik sharma  (9 years ago)

Here on Dividing 16937 by 31 we get 15 ramainder
thus now we can write
((15)^30)/(31)

Now taking 15*15 we can write
((225)^15)/(31)

on Dividing 225 by 31 we get 8 as remainder
so we can write
((8)^15)/(31)

Taking 8*8
((64)^7*8)/(31)

64%31 is 2
so
(2^7*8)/(31)

taking 2^5=32 we can write
(2^5*4*8)/(31)

32%31 is 1
so we are left with
(1*4*8)/(31)
thus it is 32%31=1
so 1 is answer

Is this solution Helpfull? Yes (1) | No (1)  

Arshal Jain  (10 years ago)

no not 30 its 24......

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suphia aftab  (10 years ago)

11 is the ans

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Guru Pranav  (10 years ago)

1 will be the remainder !!!

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padmini  (9 years ago)

use the fermet theorem a^p-1/p =1 where p is a prime number

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Sangeetha P K  (6 years ago)

Euler thereom says:
a^(p-1)/ p = 1 remainder
where p - prime number
a - natural number

In this question 31 is a prime number
So a^30/31 = 1 remainder

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