Latest TCS Aptitude Question SOLUTION: What is the greatest possible positive integer n if 8^n divides (44)^44 without leaving a remainder? a)14 b)28 c)29 d)15

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What is the greatest possible positive integer n if 8^n divides (44)^44 without leaving a remainder?
a)14 b)28 c)29 d)15

Asked In TCS Satheesh (11 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

pankaj kumar  (11 years ago)

44^44 = 2^88 *11^44
= 8^29 * 2 * 11^44
so ans is 29

Is this solution Helpfull? Yes (62) | No (14)  

Vishnu Priya  (11 years ago)

8^n=(2^3)^n
44^44=(11*2^2)^44=11^44*2^88
(11^44 *2^88)/ 2^3n
3n=88
n=29

Is this solution Helpfull? Yes (46) | No (9)  

jasveer   (11 years ago)

VISHNU PRIYA plz tell me why u write 3n=88 can any budy explain me

Is this solution Helpfull? Yes (11) | No (5)  

ravindra kumar  (11 years ago)

8^n/(44^44)
8^n=(2^3)^n
(44^44)=(11*2^2)^44=(11^44)*(2^88)
(11^44*2^88)/(2^3)^n=(11^44)*(2^88)/(2^3n)
Here 3n=88,n=29. Hence ans will be 29 bcoz 29 is the greatest possible positive integer without leaving remainder.

Is this solution Helpfull? Yes (7) | No (7)  

RAHUL KUMAR  (11 years ago)

(11*4)^44/(4*2)^n,,so max value of n from option is coming 28..plz check

Is this solution Helpfull? Yes (2) | No (4)  

Yadvendra Singh  (11 years ago)

every 44^2 is divided by 8 and gives output that is 2421 not divisible by 8 hence the answer should be 15.

Is this solution Helpfull? Yes (2) | No (12)  

Arka Laha  (11 years ago)

44^odd=last digit is 4 44^even last digit 6............
now 8^1=8
8^2=4
8^3=2
8^4=6
8^5= again last digit will 8 so in this way we can see 44^44 last digit is 6 and from options we can see max value of n is 28 where it gives the last digit 6..... so 28 is correct.......

Is this solution Helpfull? Yes (2) | No (7)  

rohit kumr  (11 years ago)

(44*44*44)/(8*8)=11*11*11 i.e. with no remainder
there is 44th time 44 and think as in grp of three maximum 14 times 44 divisible by two 8....so 14*2=28...is answer...pls confirm.. ;)

Is this solution Helpfull? Yes (1) | No (9)  

Harsh Poddar  (10 years ago)

answer is d) 15
reason-
because when we divide 44^2 by 8 there is no remainder
as it is 44^44 we can make 8^22 to have no remainder because as there is 44 times 44 and 2 times 44 is needed to be divisible by 8 so we need 22 times 8 to be divisible by 44^44
but in the option 22 is not there the number less than 22 in the option is 15 so the answer is 15

Is this solution Helpfull? Yes (1) | No (5)  

sourav  (10 years ago)

@HARSH PODDAR akhono answer korar age hoyni tr..vulval answer krbi na bkcd

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

Mohammad Sarfaraz Ali  (4 years ago)

Hello Guys hope u r doing well
8^n divides 44^44
so, (11*4)^44=11^44 and 4^44
11^44 unit digit is 1
4^44 unit digit is 6
so 44^44 unit digit is 6
if we take 8^28 whose unit digit is 6 then obviously 6%6 is 0.
So I think ans is 28

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

Aparna Sutar  (11 years ago)

ans=28.
because 44^44 and every 4^even digit divisible by 8 so maximum 8^28

Is this solution Helpfull? Yes | No (7)  

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