Latest CTS Aptitude Question SOLUTION: 2^81 when divided by 6,what is the remainder

• Placement Papers
• /
• CTS
• /
• Numerical Ability
• /
• Number System

CTS Question Papers: CTS Interview Experience(3) CTS Company Profile

(#M40034233) CTS Numerical Ability question Keep an EYE

2^81 when divided by 6,what is the remainder

Asked In CTS YAMSHI SAGIR (10 years ago)

Solved NAOREM DINESH SINGH Read Solution (13)

Is this Puzzle helpful?   (33)   (9) Submit Your Solution Number System

Read Solution (13) :

Saraswathy  (10 years ago)

2^81/6 ====> (2^1*2^2*2^3*....81 times]/6

2^1/6 ----------> remainder=2
2^2/6 -->4/6 ---> remainder=4
2^3/6 -->8/6 ---> remainder=2
2^4/6 -->16/6 --->remainder=4
2^5/6 -->32/6 --->remainder=2
.
.
.
it goes on in a cyclic manner

so remainder is "2" for all odd powers of 2 nd "4" for all even powers of 2

here 2^81 which has the odd power

so remainder =2

Is this solution Helpfull? Yes (60) | No (1)  

Rohit Agarwal  (10 years ago)

((2^3)^27)/6
==>((8)^27)/6
==>(2^27)/6
==>((8)^9)/6
==>(2^9)/6
==>((8)^3)/6
==>(2^3)/6
==>8/6

so remainder is 2

Is this solution Helpfull? Yes (13) | No (2)  

Vivek  (10 years ago)

2^odd/6------->remainder= 2.
2^even/6------>remainder= 4.

So, the answer is 2.

Is this solution Helpfull? Yes (6) | No   

NAOREM DINESH SINGH  (10 years ago)

remainder= 1

proof:
2^81/6
= 4^80/6
=2^79/3
=2^(4+75)/3
=16^75/3...
& 3|16|5
15
----
1

since 16^n/3, remainder=1
16^75/3, remainder=1

hence proved...

Is this solution Helpfull? Yes (2) | No (8)  

Harwinder Singh  (10 years ago)

2^81=2^80*2^1
so 2^80*2/6=2^8*10/3
now just take 2^8/3=256/3
which leaves a reminder of 1..so 1 is the ans

Is this solution Helpfull? Yes (2) | No (3)  

rajesh  (10 years ago)

Ans: 1 ;(2^81)/(3x2)==>(2^80)/3==>even powers will give remainer 1 and odd powers will give remainder 2

Is this solution Helpfull? Yes (2) | No   

Sohini Nandi  (10 years ago)

2^81/(2*3)
=2^80/3
=(3-1)^80/3
=(-1)^80
=1

Is this solution Helpfull? Yes (1) | No (2)  

Rahul Das  (10 years ago)

let odd power of 2 is 3=8
8%6=2
next power 5=2^5=32
32%6=2
odd power of 2 when divided by 6 remainder is 2

Is this solution Helpfull? Yes (1) | No   

SATYA SHIV  (10 years ago)

2^81===2*4^40 =16^20*2/6 =rem2*4^20/6 2*16^10/6 =2*4^5/6 =8*16^2/6=2*4/6=2

Is this solution Helpfull? Yes (1) | No   

vinay kumar  (10 years ago)

for every 4 divisivbles we get 2 so
for 81 th number we get 2 so it is divide at 0 we get remainder as 2

Is this solution Helpfull? Yes (1) | No   

Pathmavathi  (10 years ago)

2^81
2 s unit sequence 2,4,6,8,0 so totally 5
81/5= 16 quot, 1 remaindr
in sequence list 1 ll be 2
so ans=2

Is this solution Helpfull? Yes (1) | No   

jagannadh  (10 years ago)

4 is the answer...

Is this solution Helpfull? Yes | No (5)  

a  (10 years ago)

2^81/6
->2^9/6=1
->2^9/6,2^9/6. . . . .2^9/6 total 9 times each one gives remainder one
so final remainder is 1

Is this solution Helpfull? Yes | No (4)  

Please Login to Read Solution.