Latest TCS Aptitude Question SOLUTION: What is the largest positive integer n for which 3^n divides 44^44?

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What is the largest positive integer n for which 3^n divides 44^44?

Asked In TCS Trbeni (10 years ago)

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Suman  (10 years ago)

no positive integer value of n will satisfy given condition as zero is not a positive integer.

Is this solution Helpfull? Yes (20) | No (3)  

KISLAY  (9 years ago)

kripaya aapas me maa behan naa khele

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

AKASH SINGH  (10 years ago)

no digit satisifies this condition because
on dividing 44^n by 3 , we get remainders 2,1,2,1,2,....
so, for no value, 44^44 % 3^n =0

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Trisha  (10 years ago)

unit digit in 44^44 is 6. so largest value of n=2

Is this solution Helpfull? Yes (2) | No (23)  

shouritra das  (8 years ago)

Ans will be definetly: n = 0
The digit sum of 44 44 is when remainder obtained 44 44 divided by 9
44 44 = (45−1) 44
Each term is a multiple of 9 but the last term which is (−1) 44 = 1
So the digit sum of 44 44 is 1.

Now the divisibility rule for 3, 9, 27... is the sum of the digits should be divisible by 3, 9, 27 respectively. In each case the digit sum is either multiple of 3 or 9.
So for any value of n > 1, the given expression is not divisible by 3 n....

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mukesh kumar verma  (10 years ago)

(x1+x2...+x10)/10=50 and (x12+x13+....+x22)/11=40
so (550+X11+440)/22=45
then we get x11=1 ans

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Danish Shaikh   (10 years ago)

Understand this, 4 raise to 16 is divisible by 3¹, 4 raise to 17 by 3²,
4 raise to 18 by 3³....our qs is 44⁴⁴
now 44 raise to 6 is divisible by 3¹, hence 44 raise to 7 will be divisible by 3² and so on.....solving further 44⁴⁴ will be divisible by 3 raise to 39

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hemalatha  (10 years ago)

from options it will be clear 3^n divides 36

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